It should make no difference in a properly constituted scientific experiment. The problem comes with cultural bias eg.
the majority of people in a country are non religious....therefore that is considered the norm.
I think you are confusing something that is the most common thing withnit being thought of as right. This is, ironically, not uncommon and means that the use of 'abnormal' causes issues since it now has a pejorative meaning.
You also appear confused about what a control group is. It's not about what's normal it's about having a group that does not have the variable you are testing.