He’s way too old for that, that’s what toddlers do. DH isn’t doing him any favors by letting that go on. 

It might be a sensory thing, maybe look into that and find an alternative for it. I dont think you are picking on him and I wouldn't just ignore it but if it's a nervous habit or a sensory need it will need to be dealt with differently.

Tell that dummy you married that he can parent his kid and tell him it's gross or the kids at school will and that won't be pretty. Does he want his son "picked on" by adults who love him, or middle schoolers who give zero shits about him?

I’d leave this one alone. I chewed on a blankie for WAY longer than a kid should but it was absolutely something I needed. Out of all the atrocious things my mom’s husband did, I resent his trying to take my blanket away the most. Still, at 40 *cough cough* years old, I count that as a defining trauma in my life. I finally stopped on my own because I didn’t want sleepovers and friends to be awkward. 

Perhaps, insist on frequent hand sanitizer use? “It is cold and flu season! Let’s protect ourselves!” Or maybe stock a particularly yummy chewing gum? If you make a big deal out of it, you’ll get pushback.

....walk in on him with his hand in his mouth.

Does he do this when he thinks he is alone? If yes, since his dad thinks it's no problem, I'd just ask that he does it in his bedroom or bathroom with the door closed. DH should tell him that he can only do this in private and should wash his hands before re-entering common areas.

Now if he's doing it in public that's another matter. SS will definitely get negative feedback from that. I can't imagine a teacher watching that and not saying something (privately) to the child. Teachers, in general, are not fond of correcting papers touched by body fluids.

One of my sister's kids does this.  She is eleven. The difference is that she only does it at night when she is in bed.   My sister has taken her to the doctor and a therapiat.  Both say that it is an involuntary coping mechanism.  This makes sense if you know the environment that her kids have grown up in.   My sister has tried to get it to stop and nothing works.  I think my niece does it without even realizing it.  At the end of the day, your SS may be using this as his coping mechanism.  I understand that its gross but shaming him probably just makes the problem worse.  If I were you, I'd encourage your DH to take him to a doctor to address the issue. In the meantime, try and encourage him not to do it in public.  But if I were you, I wouldn't make this an escalating issue between you and DH.  

as a toddler . Those very same fingers. I was told I needed to stop her from doing it or it would affect her teeth and palate. Sure enough at 14 the orthodontist had to put his device on the roof of her mouth and we have to get a key and turn it so many turns to fix her mouth. When she was little and she stopped at say 3 or 4, I remember the pediatrician telling me to put vanilla extract on the fingers she sucked on cause it tastes bad. Easy to do on a toddler but I bet hard to do for a teenage stepson

What is he touching with that hand that is in his mouth? I cringe just thinking about it.

Do you know if he does it at school or with friends? If he can control it then it's a lingering comfort thing and you should be able to ask him to do it in his bedroom.

Frankly he's getting to the point where he's gonna do other things with that hand and not wanna stick it in his mouth. So that may solve your problem.

Not your circus; not your monkey. His father doesn't care. Let it go.