There are tons of (valid) reasons for and against boosting birthrates, but you have to break it down to the actual reasons that people are "natalists" or not.
Throwing all (anti-)"natalists" into the same pot makes as much sense as labelling communists, fascists and anarchists "anti-capitalists" instead; yes your label technically applies, but the group it describes is so heterogenous that you can't meaningfully talk about it anyway.
Edit for failing to address your actual question: No and no (people are not anti-nativists by default and shouldn't be).
If "anti-nativist" means someone that wants to keep birthrates below 2/womanlife long-term, than this is basically advocating for suicide at a species-level, and "unhealthy" from an evolutionary point of view.
But is that actually what your "anti-natalist" believe? If people just live lifes that lead to <2 children/woman, but don't really care or consider the whole question, does that make them anti-natalists, too (I don't think so)?