BBQ-style baked beans without mustard?
Just omit the mustard. In just about every recipe I have seen for beans, it is proportionally a very small component. And while we tend to think of mustard as being bold in flavor, it's really the vinegar that makes it seem that way.

You should also stray from any recipes that call for store bought barbecue sauces, as many will contain mustard.

Finally, one reason mustard appears as an ingredient in dishes like this is it is an emulsifier. You may wish to find a substitute emulsifier, making sure of course that your friend can handle it as an ingredient, to keep too much of the pork fat from separating in your mixture.