Solidarity is not for everyone.
Solidarity, as a general concept, is only for those who can be identified as bearing a likeness to the individual that is seeking solidarity. Likeness, in this case, can be of different degrees: alike in lived experience, alike in embodiment, alike in social situation, alike in sexuality, in gender, in race. Likeness, as I'm using it, isn't something that one perceives only through the senses: it is an affective feeling generated out of actions, embodiment, and the way in which an individual emerges out of its historical horizons. To this end, "solidarity" in whatever sense that it is deployed, is limited to those individuals, those selves, that appear like the individual seeking solidarity.
If we take this to be the case, then we can start to see not only how groups police who can and cannot be entered into solidarity with, but how they seek solidarity with individuals and other groups. Historically, we can point to the demand of the Civil Rights movement that Black women subordinate gendered oppression to the overall needs of the movement itself as examples of the "how" one seeks solidarity with others. In order for Black women to be perceived as being "in solidarity" with the rest of the movement, they had to conform their lived experience to that of the overall group. In so far as the Civil Rights movement was predominantly for and led by Black men, to be "in solidarity" with the movement, for Black women, was to put aside that thing that made them incapable of being "like" those who made up the moment, namely their lived experience as women. To be in solidarity with the Civil Rights movement meant that Black women needed to be Black first and women second.
Similar modes were in operation with regards to women of color (not just Black women) and Feminism broadly construed. In order for feminists of color to enter into solidarity with white feminists, they needed to articulate their lived experience as being "like" the lived experience of the white women around whose experiences feminism was organized. Because of this, feminist movements did not adequately address the unique issues that feminists of color had to deal with: they could not count on the support of their feminist "sisters in solidarity" because the expression of their unique marginalization would be to remind their "white sisters" that they were not alike as women, or as oppressed women. In so far as feminist theory continued (and continues) to treat women of color (and trans-women, and women across the sexual spectrum, and anyone else who identifies as a woman) as "(white) woman + marginalized identity," the solidarity within feminism exists only on the terms of a dominant majority.
What I'm pointing to here is the fact that solidarity, as currently deployed and constructed, relies upon the degree to which an individual can be considered to be "like" another individual in a visible fashion. When the individual's embodiment (social or physical), lived experience, or any other facet of the social and historical horizons that they emerge out of marks them a different from the group that they seek solidarity with, they must subordinate that difference to the group or be viewed as ineligible for the benefits conveyed upon them by the act of solidarity. Naturally, we can see how concepts of authenticity and essentialism enter into judgments of who can be entered into solidarity with.
To this end, the problem of solidarity is not merely inter-group, but intra-group. That is, a member of a group only remains in solidarity with that group in so far as they can maintain the image of likeness with that group. Once the individual deviates from the image of the person who can be entered into solidarity with, that individual is subject to expulsion for the group. Deviation, here, is away from the image and usually taken to be towards that which the group claims to be standing against: the less like the image the individual is, the less they can be entered into solidarity with. This leads to "how" some bodies are entered into solidarity with, especially when connected to authenticity.
For example, to enter into solidarity with the whole of Black anti-racist work, the performance of Blackness must be recognizable as being "like" the Blackness constructed by the group itself. The bi-racial individual who seeks solidarity with Black anti-racist work must then make their experience appear to align with, or be like, the group that they seek solidarity from. They must "check their white-passing privilege," or acknowledge the ways that their physical embodiment marks them as different both in lived experience and in being in the world, in order to stand with other Black people in combating racism. While I am not here to decry "privilege checking" as inherently bad, I am here to point out that it has been, and continues to be, deployed as a mode of silencing, of bringing the bi-racial (or other similarly privileged) individual in line with the expectation of Blackness so that they can be entered into solidarity with.
In doing so, the demand of solidarity that one conform excises valuable portions of that individual's lived experience: in the case of the bi-racial individual, we lose the way in which racism must adjust itself to exclude (or include) bodies that do not conform to the image of whiteness. We miss the ways in which that lived experience expands the way we think about racism. Further, this demand that people adjust their lived experience so that they can enter into solidarity holds in place a particular image of what this individual "ought" to be in order to be considered part of the group. Unless one fits the image of what one "ought" to be perfectly, the support structures that come with solidarity are denied and the individual is left orphaned. This is particularly tragic when we consider that an individual who straddles two worlds, socially, physically, or affectively, becomes a literal orphan from both worlds in so far as they refuse to conform themselves to the image required by solidarity from either group.
This is not merely an issue of race, but of gender and sexuality: my conversations with several of my queer friends has indicated the myriad ways that they have to carve away parts of their lived experience in order to be appropriately queer enough to enter into solidarity with the queer community. They describe to me how they cannot be "too cis-het" or "too straight looking" lest they are pushed out of their spaces because the do not appear to be like the overall queer community. Again, the specter of authenticity is made present: in so far as the embodiment and performance of queerness does not line up with the image expected by the community, these individuals cannot be taken to be in solidarity with the rest of the community.
I will not end this on a positive note, as there is no positive upshot unless we start changing the way in which we practice solidarity. To me, solidarity as it is practiced right now appears to be an attempt to preserve sameness over difference: it is an attempt to hold static an image of what people "ought" to be in order to be in solidarity with a community. In short, solidarity discourse becomes another mode of authenticity discourse when it argues demands conformity to an image in order to stand with the group against something that has a real impact on the individual's lived experience.