Conservative summer camp

I don't know what exactly it is about, but it certainly doesn't detract from a secular camp. Therefore, in my opinion, it is definitely important and therefore permissible to participate as much as possible. It is worth making sure that their halachic standards for Shabbat and kosher are consistent with yours (at least as far as it concerns you and is required of you. You are not responsible for what others do). As for mixed prayers, in my opinion there is no prohibition on this (although of course almost all poskim will disagree with me on this). But at most, one can always pray alone. The mission there certainly justifies it. Additionally, you should make sure that you are not asked to defend positions you do not agree with. It is a good idea to have someone on your phone or WhatsApp who will answer your questions in real time. I don't assume there will be anyone like that there. Good luck.