It's not common, no. And I've looked up this account and it's not a tourism promotional page nor anything related to the government, it's just an account by some dude that self-describes as "from the deep Castilla" posting photos of places in Spain, Spanish traditions, and praising historical Spanish army and troops in wars and invasions and saying it was better than other countries' armies.
I can't talk about all of Spain with certainty, but I would assume it's the same as here. Here in the Catalan Countries university education is VERY valued. The reason is because we come from a time of extreme poverty. Back in the time of our grandparents (the generations born before the 1960s), poverty was very generalized. Many people didn't have food every day, so lots of kids couldn't finish school because they had to work full time in factories, workshops, etc. For example, my grandparents left school at age 13 or 14. But whatever little education you could get, that was considered with great importance.
I have a grandmother who could continue to high school (working only after school), and to see what the mindset I'll give you an example she has told me many times. Back then, in schools they studied French as the foreign language (instead of English like we do now), she found it difficult and one time she complained at home saying "why do I need to learn French? It's not like I will ever go to France anyway!" (we live 2 hours by car from France, but back then this seemed like a luxury). Her relatives reprimanded her harshly for it saying "they can take everything from you, but they can never take what you know". This was something very important during a fascist dictatorship who had, in fact, taken a lot from many people.
When this generation started having kids, it was the baby boom of the 1960s-1970s. The 1960s is when things started changing, the extreme poverty of the post-war period gave way to industrialization and better material conditions for a large part of the population. And when this new generation grew up, in 1975 the dictator died. The 1980s was a new time where the working class could suddenly go to university, and people did. These parents who grew up considering that going to high school was lucky were very enthusiastic about sending their children to university, because they saw it as a way to ensure their children wouldn't go hungry like they did. University was seen as a social elevator, but even besides this, education was highly valued for its own merit.
Our generation were raised by these children, the first working class people who could go to university. Thus, the importance of education has been passed down to us. For this reason, nowadays there's the problem that too many people go to university, and as a consequence university graduates can't find jobs while we can't find people with practical formations like electricians, carpenters, machine operators, etc. But still, it feels almost "mandatory" for everyone who can to go to university, to the point that the alternatives are barely even considered by many young people.
I Gen Z is the first generation where maybe education isn't as valued because it's almost given for granted? I don't know. But either way, people are still going to university en masse.
I've searched for numbers and Spain is the 2nd state in the EU with a highest amount of people getting PhDs, only after Germany (source). So yeah, I don't think that tweet is representative of a general mindset at all. But fascists (Vox and PP voters) would be more inclined to think like that tweet. In the whole world fascist are anti-intellectual. So, considering how the person who runs that account talks about the Spanish historical troops and wars, I think we all can make a guess on where he stands.
Anyway. Of course men without degrees built that. Architecture was not taught at universities back then, it was taught within guilds. It doesn't mean they didn't have an education to be able to do it, just that things were learned differently.