Is it illegal for my employer to disclose to a customer that I receive social security benefits for a disability?

No..

Though I can't think of a good reason why they would want to bring it up.

All I know is that the Americans With Disabilities Act code is a mile thick. It could be 'illegal' but I doubt you would get any compensation.
You start at the state level and they refer it to a regional office, and 2 years later you might get something that says that the employer was told not to do it.
What you should do is tell him as politely as possible to never mention it again.
And why did he in the first place?
It's one of those things that you have to ask yourself what is worth what.
He may resent your benefits, who knows.

First why or how do they know, it is not their business if you do, unless you are claiming a disability

It is poor business practice to do so, unless they were bragging about hiring disabled people to someone