Same experience here. I stopped it almost completely a couple of months ago when the authorities from my country (EU and NATO member, mind you) have started fining people for their anti-Government FB posts. The stated reasons were that those posts were inciting people to violence, but the police never revealed the posts' contents so there's no way to actually know when one can become liable for posting an anti-Government message, I mean "lets get the Government down!" can be seen as inciting people (and a new proposed law even mentions potential prison time for the same kind of FB posts). No way I risk going through that hassle for no real benefits, as people have very rarely changed their mind based on others' FB messages.
Do it in person and don't approach it as a conversation specifically about politics - "Did you see x in the news? Crazy huh?" is better than "Here is this hilarious meme about Republicans/Democrats!" etc.
How do you be "highly political" on Facebook?
Talk about politics and seek out political discussions, same as anywhere else.
Do it in reality
That's honestly the most realistic approach. I make a conscious effort not to follow politics nowadays, too much negativity, but doing so online seems to always cause folks to fly into defensive mode. In person less so. Facial cues, maybe?