Apostate has religious overtones and a very negative connotation. Renegade is more neutral and could be used positively, whereas it is very unlikely that you will hear apostate used to positively describe someone (although you are also unlikely to hear it in general as it is not in very common usage).
@scdp in america rebel can be anyone who goes against accepted culture. such as someone with hair dyed blue. they are going against what is normal. Renegade make it seem like almost a criminal or someone on the run