Should the employer respect this?

I think a lot of employers will if you tell them ahead of time. But there's only one way to find out for sure and thats to apply and see.

 

Technically in some states they can't deny you bc of religion (along w race, gender, etc). But they can't deny you on that fact.

 

It’s a supermarket, so I doubt the employer wouldn’t let you, as Sunday doesn’t have any more or less demand than the other days. But if it was a job dependent on Sunday traffic like a sporting venue or something, that’d be a different story.