Under some variations of some denominations, once you accept Christ, you're automatically saved. This is not the case across the board. Some say that you have to have faith AND good works, or it's all a show.

Likewise, some denominations say non-christians are damned, but other ones say that if they have not actively rejected Christ and have lived a good life through the "natural law" then through the grace of God they are saved.

I am no theologian, but you're painting with a very, very broad brush. This leads directly to your bad syllogisms.