No, I get paid for my Airbnb bookings into my Canadian bank account. Mexico doesn't care where your money gets deposited, as far as I'm aware, what they care about is that you declare your earnings made in Mexico and pay the required taxes.
Now, as I said, I haven't tested this out yet, as I'm not open for bookings at the present time and since they brought in the having to give Airbnb your RFC and have them collect taxes on your behalf. But I've run a small business here for 15 years and declared all my earnings from that, and the Mexican tax department doesn't check whether my income gets deposited into my Mexican bank account, or the clients pay me in cash, or however, all they care about is that I file my income declarations and pay the required taxes.
One of the problems for you is that you haven't given Airbnb your RFC #, which means they will charge IVA @20%. If they had your RFC, as far as I read it, you'd be charged something like 4%.
@Peter-and-Wendy2