It is stereotyping, but it strikes me as much less unreasonable than other forms of stereotyping. There's an element of privilege to the matter as well.
For one thing political affiliation is a choice. No one is making you register for a political party. Much less visibly show that party affiliation. You wouldn't know a stranger was a Trump supporter unless they made their political views clear, wore Trump affiliated clothing, etc. That's not a valueless signal.
And while not every member of a party may hold the same views that might be disagreeable, they are affiliated with a party that has explicit party positions and elected party officials that have explicit positions. They are affiliated with that party for some signal or purposeful alignment of beliefs. So it doesn't inherently suffer from the usual anecdotal and generalizability issues of other stereotyping.
And ultimately the framing comes from privilege. Viewing politics as like sports fandom or a hobby is privileged. Politics touches people's lives deeply and existentially. It isn't all polite disagreements. Erring in one direction has a lot more cost than in the other direction. There's a risk asymmetry with an out-group. Why should a DREAMer not despise Trump supporters? Their candidate explicitly threatens their lives. Even if a Trump supporter may potentially not agree with that Trump policy, a lot of them do.
A narrow version of the objection seems reasonable to me. I think there are grounds for agreement with political opponents at times on some issues. And not every disagreement should be fatal to relationships. But some arguably should! I don't know how a couple could have polar opposite views on abortion. I don't think we need to befriend Nazis.
It touches me as more reasonable than drawing conclusions off of voting. Voting can be affected by the choice set and alternatives. It also can be less thoughtful/more passive, and individually less consequential. But party affiliation is more active and explicit.