It seems to me that the guys are pretty "equal opportunity" about making jokes about people or groups of people. Also, they never come across and malicious or hateful when they do.
Occasionally, a joke might hit close to home, and gives us an opportunity to either laugh at ourselves (a dying art) or get offended and belligerent.
In the two hours or so of a typical riff, there are probably dozens of jokes about other people or groups that your friend is not offended by, but that one joke that hits "close to home" (to use the phrase again) is the one the ruins the experience? Perhaps your friend needs to consider his or her thin skin when choosing to indulge in a form of comedy that is based on making jokes often at others' expense.
Ah yes, the "thicker skin" argument. Complete BS. My friends who are trans already have thicker skins then anyone I know. They have to in order to survive in a world where they have to deal with the threat of verbal abuse, physical assault, or murder at any time just for trying to be themselves.
They just want to watch what is supposed to be family entertainment (Rifftrax words, not mine) without hearing "jokes" that reinforce negative attitudes towards them.
And in case anyone was wondering why I am posting about this and not my friends, it is because they are afraid of reprisal and threats from the people here just for speaking up.
There is a contradiction between having very thick skin and being afraid to post for fear of reprisal. As a white anglo-saxon male in the US, I can't say I know how it feels to be oppressed or ostracized by anything more than a high school class, but living in the South I observe and interact with it daily. I have had friends and relatives in that position, and it is an issue that I care a lot about. I know that almost all members of persecuted groups are personally effected by jokes and attacks on them, but there is a definite difference in degree. Many people, myself included, have very strong self-esteem issues, and anything that pokes at one's insecurities can be hurtful, but sometimes those same people can develop a victim complex, as though they are ALWAYS under attack, even when the source (and they will even admit this) is clearly lacking malice. It comes from the natural human tendency to judge ourselves based on what society and particularly those voices we respect and enjoy (i.e. Mike, Kevin and Bill) have to say about us. Of course, negative comments with the intent of being negative are offensive, and shouldn't be tolerated against non-negative personalities and traits (like being transgendered or transsexual.) However jokes are a different animal. A joke can be a sign of acceptance and respect, sometimes even a lampoon of those people who hold those negative views sincerely. When a person is unable to separate this type of reference from a truly negative one it points to a strong self-validation issue. I have watched most rifftrax that have been released, and as an unbiased 3rd party, I have never heard the guys riff maliciously on any group of people.
I think that your intent here is noble and worth consideration, particularly so that Riffers are conscious of their jokes and who they may effect, but I also think that your efforts should be helping your friends deal with their internal demons. I have known many people who would be categorized as "easily offended" or "victims" and by and large they usually grow out of it (even at older ages.) Some don't, usually because their families refuse to support them, and without strong support at home they fail to find it anywhere and become of the opinion that all people should "treat them equally" by treating them differently, by giving them special treatment or exemption. The fact that your friends have someone like you to defend them is excellent for all of them. Ideally they would be treated the same as any other group in all aspects. The problem is that the groups that treat them unfairly tarnish their appreciation of those that treat them the same as any other person. I personally believe that instead of asking to be treated differently, you and your friends should start looking closely at how the world treats them and attack the areas that are truly unfair, like employment and service. Also it is important to look inward and become totally comfortable with yourself, and that will help them know the difference.
TL;DR I am not saying that your friends should "get over it" or "just deal with it," just that they should focus their energies on fighting real injustices, and not just perceived ones.