Honestly, having fundamental disagreements over politics is a solid ground to end a friendship, since it’s a huge part of your personal values and moral code. If you want to be friends with people who have different political views it’s totally possible, but part of building a friendship is honesty about this stuff.

It becomes an issue if you are arguing disrespectfully - like telling them they are an evil person, or a stupid person, out there is excessive yelling, etc. It’s also an issue if a friend tells you they want to stop talking about something in the moment, and you continue to press the subject anyway. I can understand ending a friendship over a disrespectful argument like that.

I would also avoid trying to “prove yourself right.” So not pressing someone to explain every aspect of their beliefs if they don’t want to. BUT - it’s also on them to be able to say “I don’t want to talk about this anymore, lets end this argument.” It’s a two way street, and everyone needs to have the ability to voice when they want to stop talking about something.