Mexican Utility bill + Italian passport is assumed Mexican resident for the purpose of CRS. Citizenship is out of scope. The CRS report goes to Mexico, and they treat you as non-resident. Banks send double or false reports all the time. If the Mexican taxmen look into it in depth, and suspect you're up to some tax games, they can forward the report to Italy through TIEA. Also Italy treats you as non-resident. Quite a few links in between the bank and the jurisdiction that has a legitimate tax claim on your world-wide revenue.
Banks are required to ask for "Proof of Address". Utility bill,︀ voting card, or similar. The problem is that Proof of Address proves nothing relevant. Its︁ a worthless compliance burden on banks yet some commies think street address is relevant. It︂ only causes problems to students abroad, cross-border commuters who find it difficult to get a︃ bank account, yet it does nothing at all to crooked tax evaders 🙂
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95% of︄ banks ask for Passport, Utility Bill and Phone Number. Don't go to CIM which is︅ known as the bank of offshore companies, especially if they ask for more documentation such︆ as the AIRE card. And if you're lawfully registered in Italy as non-resident, why are︇ you asking me this question - you should already have the AIRE? As "resident of︈ Mexico" but in substance just a real estate investor, open an account with BBVA or︉ other high street bank in Spain.