Just like transgenderism why aren't mental health services all over this?
Well, regardless of any policy points or guidance (or lack thereof) from the government or medical experts, the main barrier to CAMHS doing anything is being incredibly under-resourced and being under a huge amount of pressure to meet patient needs.
Even if they had a definitive position on "this cultural issue is detrimental to children's mental health and well-being" (which they don't currently), I know that our local CAMHS at least wouldn't have the resources to manage a public outreach campaign on the topic. Obviously they will do their best to see the kids who get really damaged by this kind of thing when they can get to them, but most don't have the resources for outreach projects.
Aside from not having the resources, it's worth remembering that, as PinkNews have pointed out, many furries are also LGBT, so the NHS (which is already well and truly captured by gender ideology in many areas) would be incredibly wary of saying anything that might be construed as suggesting that LGBT people are groomers, etc.
This kind of thing would need to be dealt with at a central government level as NHS and social services are too captured to turn around and say "hmm, that doesn't seem appropriate for children and raises some potential safeguarding issues" at this point, even if individual practitioners might be thinking it.
I think that sex education materials being examined by the government (and being able to be scrutinised by parents and the media) and being put back on track through statutory mechanisms is the way to go with this one, as I'm sure there are probably organisations legitimising this stuff in schools and NHS training similar to the genderbread stuff.
Child safeguarding shouldn't be an issue that mental health services or anyone else needs to campaign about to persuade people - it should be statutory that dangerous and age-inappropriate stuff isn't promoted to kids.