Adding to what others said — if you specifically want Monero (which makes sense from a privacy perspective), there are a few options that have matured since this thread started:
Haveno is a decentralized exchange built specifically for XMR. Desktop app, runs over Tor, no account creation at all — you're just an onion address. Trades use 2-of-3 multisig escrow so there's no trust required. Two networks are active right now: RetoSwap (more liquidity) and DawnSwap (lower security deposits). Both support bank transfer, cash by mail, and in-person trades. The downside is it's desktop-only, so you'd run it on a separate machine or VM, not on your phone.
For wallets that actually work well on GrapheneOS: Monerujo from F-Droid is solid — has Tor support built in through Orbot, and you can connect it to your own node. Cake Wallet also works fine in a sandboxed profile if you install via Aurora Store or the APK from their site.
The trick with Monerujo on GrapheneOS is to run it in a separate user profile with no Google Play services, connected through Orbot. That way the wallet traffic goes through Tor and there's nothing else in that profile that could leak metadata.
For actually buying without handing over docs, Peach and Bisq (already mentioned) are good for BTC. For XMR specifically, Haveno is the main option, or you can find P2P traders on places like XMRBazaar who do cash trades. The premiums are real (usually 5-15% over market) but that's basically the price of not being in someone's database.