This really drives me nuts, and I think there’s multiple important dimensions to why people in the fandom react this way. I've got a pretty length examination of this--not looking at textual evidence, but moreso a meta-commentary on how people in fandom who dislike it often tend to respond to TechPhee--so I'm putting it below the cut.
1. There’s obviously a huge element of misogynoir at play here.
It’s not just that Phee is a black woman, but specifically that she’s a confident, extroverted black woman. She’s not shy, not demurely waiting for a man to express interest in her, she’s the one who expresses interest first. If she had been a white woman who behaved the exact same way I could see there being some misogynistic pushback to behaving in what’s not a traditionally feminine way while expressing with romantic interest in a man, but the fact that she’s black really expounds the matter. Black women are of course put under an even higher amount of scrutiny, expected to behave extra feminine to counteract the way they’re historically masculinized in order to be viewed as acceptable.
Look at it this way: Phee, as a pirate/adventurer with a heart of gold, is incredibly similar to Han Solo, only with a stronger moral compass from the beginning. And the way she flirts with Tech has nothing on the combative, occasionally even belittling way Han flirts with Leia. Has Han as a white man ever been subject to nearly the same amount of criticism? (Admittedly, maybe because it’s a nearly 50-year-old movie, but the enemies to lovers nature of Han and Leia’s relationship is certainly, I think, more accepted--and yet the much less antagonistic relationship between Tech and Phee is not!).
2. There’s an issue in the fandom with Projection, rather than interpretation.
Something I’ve noted in a lot of x reader or x OC fic is that people have a tendency to create characters who essentially respond to projections of what they (with all their often misogynistic and racist biases--and remember that these biases can be internalized and unconscious regardless of someone's gender or race) believe the Character needs or deserves. Rather than take things at face value, people have a tendency to uncharitably interpret Phee as a character and her interactions with Tech because they are (often unconsciously) seeking to diminish the validity of the relationship in order to keep filling that gap with their own headcanons and self-inserts.
This isn’t exclusive to the Bad Batch fandom, of course, but it’s perhaps more noticeable because of the stark gender dynamics of a largely woman-led fandom that surrounds a group of five men and one girl. There is a preponderance of self-inserts or OCs who are essentially subservient to the needs of the canon characters. Sometimes they are empty shells so that people can project themselves onto them; sometimes their traits are designed entirely to be secondary to that of the main character--head over heels in love, unconditionally supportive, soft and infinitely understanding, essentially with no needs of their own. Often any imperfections they have are less undesirable traits, more sad back stories that are easily explained away and infinitely palatable and even endearing to both readers and the characters themselves.
You see this a lot with the way that these OCs or x reader fics show interactions with Omega. I’ve mentioned before how much I hate the idea that Omega somehow needs a feminine influence or maternal figure in her life (a hugely heteronormative idea, since it suggests a family led by only men can’t fulfill the needs of any female children or that femininity is some sort of eternal ideal that all young girls subscribe to or have needs related to). Many self-insert characters are just immediately welcomed as this special maternal influence they’ve all been waiting for, who will serve the romantic needs of the pairing and the familial needs of Omega. And there's nothing more than cursory pushback on this among characters such as Hunter who are notoriously suspicious of the people they encounter.
And when a character is created who doesn’t match up onto that, especially a black woman, some fans will do anything they can to uncharitably interpret that character’s actions in order to create a narrative that will allow them to reassure themselves their their character (or they themselves) are the One True Pairing that is right for Tech. The thing about Phee is that from the moment she’s introduced, she exists primarily as herself. Besides flirting with Tech, she doesn’t express much immediate interest in the Batch; she has her own shit going on and pops in and out of the main narrative. She often acts contradictory to the expressed desires of the main characters, entering into conflict with them—but the conflict isn’t antagonistic, it’s a normal conflict between people with different interests, desires, needs. Her relationship with Omega has elements of mentorship, but it is much more like a family friend or an aunt than anything maternal. In short, she exists as herself; she’s not easy to project upon. And for someone who's romantically interested in a character as beloved as Tech, that's something that a lot of people resent. Speaking of projection...
3. Tech’s neurodivergent character traits are often infantilized or projected upon.
Here's the thing about the Bad Batch: in a short, ensemble show meant for general audiences in which we resultingly don't get a huge amount of screen time dedicated to the development of each character, there is a lot of room for projection. This is also, of course, a wider issue with media literacy among fandom--people struggle to separate themselves and their own feelings or how they would feel if they were in X character's shoes from what we actually see about how each character behaves on screen, and the less space we get for explicit character development the more space there is for headcanons and projections that have no actual basis in the source material. People can, of course, play with their dolls however they like--but when it then comes to actually making assertions about what is happening on screen, it can lead to interpretations that are completely divorced from the evidence.
I think this is something that has happened a lot with Tech particularly, both because he's so beloved and because he's not always very explicitly expressive in his neurodivergence. He very rarely comes out and says how he's feeling, and such we have to rely a lot upon reading his actions, behaviors, mannerisms in order to interpret his personality. As such, there's a certain infantilization or woobification of Tech, especially based on stereotypes around neurodivergent nerds; one only has to look especially at fics or posts responding to the early seasons of the show to see people who interpret him as weaker than his teammates, worse at combat or other soldierly, with low self-esteem, etc.--all of which is directly contradictory to the early evidence of the source material and gets much more explicitly undermined in season two.
This of course gets projected onto his feelings about any sort of romantic pairing. When Phee comes on screen, ultimately I think the interpretation of her expressing romantic interest as harassment has an origin in both projection on Tech's less-than-explicit reaction (people see that behavior and think that they would not like Phee hitting on them in that way, and therefore that Tech cannot possibly like that either) as well as infantilization of his character (Tech, as a neurodivergent person whose social skills are lacking, cannot possibly either understand what Phee is doing and/or does not know how to spurn her advances, and is being made uncomfortable).
This, of course, completely ignores the fact that Tech is an adult, genetically enhanced supersoldier, who is currently a mercenary on the run from an evil Empire. He knows how to deal with an uncomfortable social situation, whether that involves ignoring it, avoiding it, or expressing disinterest in it. He knows how to stand up for himself. He isn't a child.
(On a personal note, this is something that particularly bothers me about the reaction to TechPhee, as an outgoing woman with an anxious, awkward husband who had to be the primary instigator of our relationship. I'm sure that, for some people, the way that I express romantic interest is a bit too much or not something they're interested in. During my youth, there were certainly times when people told me explicitly that they weren't interested and so I stopped flirting with them. This is a normal, mature thing to do, and making people uncomfortable briefly or making them feel not interested does not constitute harassment. For my husband, however, the way that I interacted was ideal. I was explicit and upfront about my interest, leaving very little to the imagination, which is something reassuring to him--especially since he wasn't even completely sure I was hitting on him until we were actively making out. In the explicit ways that Phee hits on Tech and the more subtle ways that he reciprocates, I see a lot of my husband and I's relationship. Everyone is different; their interests and mannerisms are going to be different; that's fine. You don't have to be romantically interested in anyone. You can say no thank you. If you have a lot of trouble with this, it's an important skill to work on. If someone is hitting on you repeatedly after you gave them an explicit no, that constitutes harassment.)
There are a lot of factors at play in people's often visceral reactions against Phee. Many of them are influenced not only by (internalized) misogyny and racism, but also by Tech's neurodivergence, the influence of stereotypes rather than textual evidence on people's interpretations of characters, and the way that fandom often promotes projection or headcanons over actual engagement with the text. While people are certainly free to engage with creative works the way that interests them, personally I'm a fan of the show because of what happens in the show, not because of what I imagine happens in the show.
If you have a visceral reaction to a character, I really encourage people to take a step back and interrogate their feelings. You're allowed to feel things, but sometimes our feelings are influenced by unconscious biases, by misinterpretations, or by projections. You may find that you're negatively interpreting Phee's behavior because of unconscious biases on your part, because of sexist or racist ideas about how a woman should behave.
Or, if you don't like TechPhee because you have a crush on Tech and want to imagine yourself dating Tech, and Phee is getting in the way of that for you, that's fine. It's a fictional show. You can imagine anything that you like. But allowing those feelings to interfere in such a way that you're making bad faith readings of the text or relying on what you imagine a character feels rather than the evidence of what we see on screen is going to hurt the way that you engage with fandom and with media in general.