Please don’t try to friend your TA, especially if you’re still in class with them. We are your instructors, not your friends.
Do you think this applies even if you’re not in their class anymore and not likely to be in the future? (Eg: if you’re a senior in a program in which classes only have TAs in the first couple years of the program?)
Generally that seems okay, although a TA getting a friend request might not know that. The bottom line is just to use caution and don’t be offended if a TA doesn’t accept your request. It probably has nothing to do with you as an individual.
I would just urge students to remember, at least for the duration of their being in class, that although their TA may not look or be that much older than them, the relationship is not one of friendship or peership unless they get the okay.
I don’t want to say that personal contacts are never acceptable—I love it when I see former students on campus and they tell me what they’re up to—but I do think students can sometimes be confused about the nature of the relationship, especially if a TA is younger and/or female-presenting. And e-mail and social media is often the place where this confusion plays out explicitly.