(looks not based on dressing style beard or moustache but face cut)
Answers (2)
For some religions yes. For example, some Jews still wear the hat on their head is to show respect to God, they grow facial hair and they only shave while mourning a loved ones death.
However, in Christianity there is no distinct way you have to look. Though people still like it better when you are well groomed and dressed nicely and you don't have to have facial hair.
If you're asking whether religion is in the DNA and bone structure, then no! Absolutely not!
It is true that some tight knit ethnic groups that share religion might have some similar features, such as ethnic Jews. However, it is important to understand that religion and underlying appearance have no direct causal link to one another.