In this quote how is Parris afraid to conform to society and how does this relate to his reputation?“Parris; Thomas, Thomas, I pray you, leap not...

I wonder if perhaps you left a word out of the question.  I think that it should say something like "afraid not to conform to society."  To me, the quote (along with the rest of Parris's character) shows that he really wants people to think that he is normal and is therefore worthy to be their minister.

In this quote, Parris is begging Thomas Putnam to stop talking about witchcraft.  He does not want people to think that this sort of thing goes on in his house because they would disapprove of him so strongly.  He thinks that he has to be a good example if he is to be a minister.