Perhaps you have tried this already, but if not it may be worth a shot. For a lot of people, they want recognition. Arguing will be no good, but instead of butting heads with your step dad just say that you recognize that there are serious disagreements among experts about the best plans for nutrition and exercise. That being the case, you can see why he thinks the way he does, but you are trying a different way. If you find out you are wrong because of the results, you will try his suggestions. When he says wacky things about diet and exercise, just smile and nod, then do your own thing anyways. Oh, and move out as soon as you can.
Another route is just to put money on the line. You make a prediction of the results you will get from your diet and exercise plan, he makes a prediction, find clear measures and/or a good judge, and put money on it. If he says you will get fat eating that way and you think you with get jacked, then pick some measures, put the money down and don't waste time arguing about it that could be better spent eating and lifting. I've found most people shut up when you suggest putting money down, and that failure to put money down admits ignorance and bullshitting that you can always call them on when they bring the subject up again ("Oh, you wanna bet now?"). Again, no argument is necessary, you each just have your beliefs and need n0t convince the other of anything, just lay your money down.
In any case, I'm sorry you are not in a more supportive environment and for your mom's illness.