This is a tough one for me.
I don't give a fuck as to what political views a girl has if it's just a hookup or we're friends with benefits. And I don't care what political views my friends have either.
But serious, long-term relationships might be a different story. I couldn't date someone who refused to call my trans friends by their preferred pronouns in conversation or was discriminatory towards a gay couple who I am close friends with, for example. It could be argued that such behaviour is far more of a petty and pointless bigotry disguised as a legitimate political belief than a political ideology, but I digress. Another thing to keep in mind is that some people will hide or alter their beliefs (and other things about themselves, obviously) to better align with that of their partner/prospective partner. But that is an honesty issue, not specifically the issue of differing beliefs.
Could I date somebody who believed that the 2020 election was rigged? I don't really care about that viewpoint as a non-American, but the people who hold that belief tend to have far more diffusing issues as
@jasperkent and
@Jerry Atrick implied.
Could I be in a long-term relationship with someone who is anti-vax? Probably not, I think that denial of medical science would annoy the fuck out of me as someone who is pursuing a career in medicine.
I think that the issue here is more that certain political beliefs are indicative of toxic/undesirable/incompatible traits in a person than anything. The link between personality traits and political beliefs has been studied a fair bit. We'll use the Big Five model here to simplify things.
Liberals tend to be more agreeable, extroverted, and openminded, conservatives tend to be far less agreeable and less open-minded than the population but more conscientious.
Authoritarians tend to be high in neuroticism. And libertarians tend to be very high in openness but somewhat disagreeable.
For example, I personally am very high in openness, high in extroversion, somewhat below average in agreeableness, somewhat high in conscientiousness, and neuroticism is probably average range but really depends due to episodic mental illness. My agreeableness has increased drastically (still slightly low), my conscientiousness has increased, and my neuroticism has decreased in recent years, and with that I have shifted from right-libertarianism towards something approximating a belief in leftist anarchism and community governance.
I could certainly date a girl who was a liberal or libertarian and probably even a conservative (Canadian conservatives tend to be a bit less nutty and radicalized than their American counterparts) But someone who was extremely authoritarian would probably clash with me poorly, as I have low tolerance for extremely neurotic people who like forcing those views on others due to trauma.
Someone who was extremely agreeable or disagreeable would also obviously be difficult to date long-term, since I don't want somebody whom is very overly argumentative or whom agrees with everything I say to the point that we can't even have a proper conversation.
But yeah. For me, it isn't the beliefs themselves that I really care about politically beyond a certain point. As long as somebody generally holds my basic values, I don't care how they identify politically or what their views are on taxes or firearms laws.
Religious beliefs are a bit of a different story, as I wouldn't want somebody who would give me an ultimatum about converting to/practicing a religion.
There will be punishment for treason. Most everything else is fine.