How normal would it be for reading glasses to cause blurry vision when view at a distance?

Yes: If you are looking in the distance through the glasses. If you have blurred vision in the distance when you look around the reading glasses, the glasses prescription is incorrect.

Yes: Reading glasses simply change the plane of focus of your eyes from distance to near. That's why they help with reading. Removing the glasses moves the plane of focus back to distance. When we're younger, we can do that ourselves with the lenses in our eyes. Usually, in your 40s, you start to lose that ability and need glasses to help.