I'm not sure you're fully accounting for gender dysphoria here. If you are an anything--let's say you're an owl--and it feels deeply important to you to be a (human) woman, then what happens if owl-women aren't women, in at least most contexts, is that this deep need isn't met. At least not as well as it would be if trans-species women were human women. The principle is that the dysphoria is largely dysphoria about not fitting into a category.

Now, that said, the other concerns you mention don't just go away. For instance, if an owl has murine-directed species dysphoria, and wants to be considered a mouse, but still looks like an owl, the mice are understandably going to be really freaked out. Even if the mice in the know eventually come to learn that this owl really "is a mouse", every interaction between strangers (trans-species mouse + cis-species mouse) is likely to engender real and deep distress.

Of course, I've deliberately chosen an extreme, and therefore unrepresentative, example to illustrate the point. The reality is not so stark.

But the issue remains: you can't balance the value of feelings of safety on the one hand with feelings of dysphoria on the other hand if you don't fully acknowledge the latter.

(Then another issue arises, which is whether there can be degrees of strength of gender dysphoria, and what to do in those cases.)