1. a fair, objective, and permissive attitude toward those whose opinions, practices, race, religion, nationality, etc., differ from one’s own; freedom from an understanding
2. favorable reception; approval; favor through understanding.
"I accept that what you do behind closed doors as your business, but I would try to persuade you in the other direction every chance I got."
“I accept you — in spite of your sexual orientation, gender identity, ethnic background, religion, pathetic bank account, unimpressive job, really bad hair.”
Option number 1 is to not even make an attempt to be around this individual. Whether that is through exclusion, judgment, or distance, you have no intention of trying to understand where s/he is coming from. His/her beliefs are too far removed from your own that you don't even want to try.
Options number 2 & 3 are to tolerate or accept this individual. There is a reason why I want to talk about these two together. Whether you tolerate or accept this individual, you are making an effort to continue a relationship with him/her. Even if it's, at the basic level, keeping them as a civil acquaintance. But here is where the similarities come to an end.
"I don't understand your beliefs, but know they are different than mine, so I'll just put up with our differences."
"I understand that your beliefs are different than mine, and I still love and respect you."
In my opinion, the huge effort our country has put into the use of the word, "tolerate", most likely has an agenda behind it.
Tolerance is the mother of bigotry.