Do they allow consular id cards?

I assume you are referring to the "matricula consular" photo ID card issued to Mexican citizens residing in the United States. Their acceptance varies by jurisdiction. I have seen them accepted in New York City for purposes of cashing a check, opening a bank account, showing ID to a police officer, using a credit card at a retail store. I have also seen them rejected by bar bouncers as not being sufficient for proving age. I believe some of the new Arizona-style state Immigration statutes stipulate that they are not to be accepted for any purpose as legal identification.