I completely agree - don't show your disapproval. My DD had bought home some complete frights in her teens. Its hard to do but don't react to them. Just be pleasant and pretend you like him and she will soon see him for what he is. If she gets wind that you and her Dad don't like him it will make him all the more attractive. Your DH should be pulling her up for her rudeness though - that isn't on.
My DD had a BF who didn't like me. Like your DD she was infatuated with him too. It turned out he didn't like many other people either - he basically had almost no friends.
I'm not a step-parent so I don't have direct experience of your situation, but from your post I don't think this is a stepmum problem. This boy would probably have caused problems anyway.
The difficulty you have is that your SDD won't want to hear any criticism of her BF and anything you say that's negative about him may make him seem more appealing.
I know it's really difficult, but the best you can do is to be very nice about him, encourage her to have him spend time at your home and take comfort from the fact that she'll be learning valuable life lessons from her relationship now, rather than when she's older and it's all more serious. Try not to visibly react too much to things she claims he's said.
It probably won't last. Also remember that teenage girls love to make dramatic statements. I had a row with my DD about her BF during which she announced she'd like to move out. The very next morning she had a horrible cold and was cosied up on the sofa accepting all my offers of TLC. She hasn't mentioned moving out since.
Make it as easy and appealing as possible for her, without being it obvious to spend time doing other things with you or her friends or doing any hobby.
My DD's BF broke up with her shortly after lavishing time and money on her birthday. Despite the all-consuming nature of their relationship she bounced back quickly and my relationship has not suffered - if anything she knows I'll be there for her even if I don't agree with the choices she's made. Hold your nerve and this will blow over.
Around 4 years ago I married a man who already had a daughter from a previous marriage. His daughter was 12 when I married him and for the first few years everything was fine, until she got her new boyfriend.
He was an old primary school friend who she found on Facebook. When they started going out I thought it would be good as she doesn't have a lot of confidence so I thought it would help. However, a few weeks into the relationship he started being rude to me about how I wasn't her 'real mother' and therefore have no control over her. After that things spiralled out of control and she started being rude to me too. She went on about how I wasn't her 'real family' and now I had 'stolen' her dad away from her.
She is infatuated by her boyfriend and I am terrified that she will run away with him. She has threatened so many times.