Well,
1. Again. It's not a slippery slope, it's present day statistics. It's only a slippery slope if it's along the lines of "if we allow/disallow X, then we'll allow/disallow Y". E.g., "if we allow homosexual marriage, next thing we'll be allowing paedophilia and bestiality." If it's about present day statistics, there is no slippery slope. E.g., saying that the 3% of drivers that are unlicensed cause 18.4% of fatal accidents is not a slippery slope.
2. Then we're back to: how do you know who is that sincere and who not? Simple scenario: You're a woman in the women's locker room at the pool and someone looking like Chad Thundercock in a wig enters. How do you tell if it's someone who is whatever you count as a sincere trans woman, or some cis male perv who just wants to see women naked? Honest question.
You keep answering that yeah, but trans knows in their head if they're that or not. And sure, I'll grant that. But without having mind-reading powers, how do YOU tell?