As I see it, there are non-KYC services where you can change BTC to XMR or XMR to BTC.
According to my research, e.g. changenow.io seems a KYC exchange, but they don't ask your documents, only in case of suspicious transactions. Or do you know surely non-KYC echanges with BTC <-> XMR change possibility?
Decentralized exchange: Bisq
Instant swap: exch.cx
You need to read the terms of service too, some exchange even though not asking KYC but they're combating against illegal funds, but if it just for protecting privacy, it's fine.