After months of debate, controversy, and a threatened Brad Pitt lawsuit ... the so-called Straight Pride Parade is underway in Boston.

The parade organizers -- a group called Super Happy Fun America -- claim straight people are an "oppressed majority" and believe "the day will come when straights will finally be included as equals among all other orientations."

Those kinds of statements made many think the whole parade was just a troll, and not something that would really happen, but there are several hundred people lining the same route of the Boston's Pride Parade back in June.

The Grand Marshal is, ironically, the openly gay, but extremely conservative, Milo Yiannopoulos.

Counter protesters have assembled in Boston in response to the straight pride parade and we’ve got music y’all. 💙💚💛🧡❤️💜 pic.twitter.com/TUW03TfY7I — Erin Spencer (@erinspencer93) August 31, 2019

Protesters are on hand as well, but don't appear to be confrontational. Hell, they brought musical instruments.

Still Boston police are out in force ... just in case tensions rise and anything goes down.

You'll recall, earlier this year the parade organizers used Brad Pitt's face on promotional material ... calling him straight America's mascot -- but as TMZ first reported, Brad wasn't down. He threatened to sue if Super Happy Fun America didn't cease and desist. They did.