I disagree wholeheartedly. If you put this in your application, you actually put yourself in a position to publicly disclose it. If you see some of my other answers about sensitive topics in an application, I have responded the same way that if you ever do, you have to be able to discuss them and they are a matter of commentary. Now, FERPA does shield from some of this, but this would be a public organization that the Op is a part of in the application. That public organization disclosure would not be considered private, though it would not be volunteered unless directly asked. In fact, whatever groups the Op worked with if they are officially sponsored student organizations would be disclosed under a FERPA request.
I'll use a less problematic example to illustrate. Say that I am a member of the ASU College Republicans which is an official ASU organization. This would not come up with Student Services on my transcript, but it would come up if someone intentionally asked for the membership of the ASU CRU which as a student organization, the membership, officers, and charter are disclosable and not FERPA protected as it is supposed to be open membership.
Op, if you are going to participate in an open community, you always run the risk of having that community in your private life, like it or not. By choosing voluntarily to participate in those communities, you choose to be involved with being identified with them. From others who went down this road, I can tell you that this does not usually end well. You need to be prepared for disclosure. Hopefully, you get the opportunity to do so yourself, but if you are going to participate in an community, that may end up being a situation where disclosure might be forced.
The health professions are probably the most understanding of those circumstances, but we don't think about it ourselves. We have quite a number of openly LBGT faculty and administration, and they themselves have accidentally outed others in casual conversation because they do not realize that they are in the closet which has caused some personal issues. You run two risks of disclosure: someone accidentally outs you to your family which is innocent from them ("Yeah, Op is a real advocate for LBGT care sensitivity issues.") but still gets you in trouble or your family is suspicious enough to ask probing questions, where FERPA in this case will not protect you.
Unfortunately, you do live with the burden of a non-understanding family which you should have some contingencies for in case disclosure happens. Again, if you put this in the app, it is open for discussion. And a matter of this sort would not be a standard report, but no one is going to protect you if directly asked as that participation is voluntary. Also, if your parents are fairly adept, they would make you sign the FERPA release contingent on funding.