What do you call a person who is against the teaching of the church?

Heretic.

It really depends, though, if that person is teaching a contrary idea, or if they just don't want to follow what the church professes.

By definition, a Heretic is someone who teaches a belief that is contrary to church dogma. A Blasphemer is someone who is irreverent or disrespectful to the church. A Heathen is someone who refuses to believe what the church teaches.