If we generate an ACH debit and send it with an effective date of the following business day, can the receiving bank elect to charge it against the customer's account on the day they receive it, instead of the following day that is listed as the effective date?

For example, we generate the file and send it on the morning of May 9th, with an effective date of May 10th.

The receiving bank gets the file in the afternoon of May 9th and posts it against the account of the customer the same day, even choosing to return it NSF if the account doesn't have funds to cover it. (Even though it would have been fine if they posted it on the actual effective date)

Is this allowed or is this a violation of the ACH rules?

I assume you are saying the effective date and the settlement date are the same? I would review Article 3, Subsection 3.3.2, Timing of Debit entries. This is not allowed.

RDFIs can post credit entries early but are not allowed to post debit entries before the settlement date of the entry.