There are things that are controversial or debated and Facebook and others stay away from that.
Advocating injecting bleach or eating albinos to cure Covid is one thing while arguing the amount of asymptotic transmission is another thing entirely.
Note I’m not making a judgement about these statements, merely using them as examples of things that absolutely won’t get you kicked off of Facebook for advocating.
Battered women shelters also dont always have exclusively female staff. They do lean more female afaik, but penis won't prevent you to work as lawyer, psychologist, security etc.
What that worry shows mostly is that whoever is creating panic about this one was never interested in domestic violence - nor even curious about it.
So your claim they “stay away from” controversial or genuinely disputed topics is plain wrong: they censor those topics heavily on FB and YT to shape narratives — from COVID to Amber Heard beating her spouse.
Your idealized “just a little” censorship has already been exceeded — showing why it’s impractical as a political idea: it’s inherently unstable.