"Ignore them." I put it in quotes because it's a lot more complicated than that, but I'm not exactly being sarcastic. You should accept them which unfortunately means not taking anything that happens too seriously, and you need to ignore it (in fact, that goes for real parents too sometimes who yell and get riled and upset too easily when if they just "cared a little less," they'd end up with a kid who trusted them who felt a little MORE cared for.
The other thing is to INCLUDE the mom. I know this sucks, but I just read something similar from a woman who wrote that she was the step-mom and a "society-accepted" type of mom (cooks, cleans, cares what her kids wear, doesn't let her go to overnight sleepovers), and she also had FULL custody with the dad, and the so-called "unfit" mom (drugs, drinking, problems galore with men, promiscuous clothing, and no idea of structure for children. What she did NEXT tugged at my heart so hard, I started crying ...
She called the mom and said, "Kari wants to go to a Britney Spears concert but it's in the middle of the week and I think it's inappropriate for a child to stay out so late on a school night, but I wanted your thoughts. What would you do?"
Well, of course the mom said that she'd let her kid do whatever she wanted, wear whatever she wanted, and go whatever she wanted. So on that special occasion (obviously not for every situation because the mom wasn't part of her life at all), she said, "Kari, I wouldn't have said yes, but I spoke to your real mom and she thought it would be okay, so I'm going to let your real mom decide this one, and we are going together to the concert." (The real mom wasn't allowed to see the child).
Oh, my. You can imagine how hard that would have been for the stepmom to basically lose her pride and her beliefs for the benefit of the child -- allowing the child to have a "relationship" in a virtual way (since she wasn't able to see the mom, or the mom didn't see her) and she did it a few other ways as well (allowed the step-daughter to wear SLIGHTLY more trendy (i.e. promiscuous) clothing, although obviously she vetoed 99% of the other things that the daughter wanted (strict curfew, strict clothing ideas, strict TV, strict healthy eating, etc).
I think that is the WORLD's greatest stepmom and if I'm EVER in that position, I hope I act with that much generosity, selflessness, and acceptance!