Now, you are asking them to automate conversions using a 3rd party exchange. Where things CAN go wrong, KYC can be sprung on you and so on.
From what I've seen and understood there, this AnonPay is an app of Trocador, and this Trocador is an "exchange aggregator".
Yeah, this is a big issue, and as a merchant you
must inform your customers that this is what is happening before you allow them to pay.
Let's say I go to a merchant and pay in bitcoin, and my bitcoin was actually sent directly to some third party exchanger to swap it for some altcoin that the merchant wanted instead. That third party exchanger takes some issue with my payment, so freezes my payment and demands KYC, which I'm not going to provide. I'm now out of pocket and the merchant will refuse to hand over the goods, since my payment hasn't reached him. But I would still blame the merchant for this, for if I knew what was happening and that my coins being frozen were a possibility at all, I'd never have used said merchant in the first place. There have been more than a few scam accusations I have seen against such exchange aggregator sites because of exchangers they have listed freezing funds for arbitrary reasons, and usually the exchange aggregator is less than helpful in resolving them.
The whole concept is a good idea, but the risks involved in the current implementation are too high.