I think you will find that safeguarding measures are very much a feminist concern.
However, this:
"this is akin to religious people using outdated texts in order to persecute gay people...but you'd probably think that was reasonable too"
is something that shows that you have little true understanding of safeguarding. Plus, it looks more like you are indulging in your own prejudice here by bringing in an irrelevant comparison. Safeguarding is needed to protect people who are attracted to the same sex as much as those who are attracted to the opposite sex.
No one is 'persecuting' people with transgender identities. Plus, of course, no one else should be coerced in any way to act as if they share the philosophical belief that someone has a gender identity. There are no biological or neurological markers that are shared amongst all people with transgender identities. Therefore, the only commonality is the belief they share about their personal identity.
Discussing whether there will be appropriate safeguards in place at a camp for children will also involve whether those children are directed to use another person's preferred language. It is important to discuss this because the English language conventions are to use sex based pronouns not 'gender' based pronouns.
If you, personally, wish to support others by not following the English language conventions that is your choice freely given. In a case where there is some kind of negative ramification to someone who chooses to observe sex based pronouns, this is a safeguarding concern.