I lived in the US for 26 years and never witnessed anyone pay with a check at a grocery store or other similar retail establishment past the mid 2000s. I assumed they were no longer accepted?
Most people will pay with either cash or card because it's more convenient. But I haven't heard of anyone that refused a check, unless it's a rather large transaction and they're concerned a check will bounce. I myself used checks and not cards for a bunch of years.
Are you in Europe? I hear it's unusual there. In the US virtually every store will accept a check. There are still stores that will not take any card. And some stores that will take a a debit card but not a credit card. But they'll all pretty much take checks.