You should always have a little clearance to the closest point a tire comes on your bike. If you run through some of the gumbo mud that sometimes washes over a road in places here after a hard rain where excavation was going on nearby, then I'd expect to come to a sudden halt. And I have in the past.

If the difference of where the tire rubs and the greatest clearance it has is a lot, then you might not have the tires seated properly. Or you have a bad tire that has damaged casing or something that shouldn't have passed the makers quality control checks.

If you need too, go to a smaller width tire. the difference of one tire size isn't going to be a big deal. Depending on what tires you are comparing. The range of riding comfort within the same size tire varies greatly. And surprisingly to many, it's the racing tires that are supple that have the best ride quality for comfort. And as long as you don't live where goat heads abound, their flat protection is more than sufficient if you want to stay with tubes.

Also, if you bought a tire that has a heavy tread pattern or a thicker tread for puncture protection, that probably has a wider overall circumference or diameter than a tire that is slick or has very little pattern. On paved roads you don't need any tread pattern.