as always, you ask good questions and make good points, but I may see a serious degree of difference in your examples and what we have here, if I may...
on the tobacco example, you are correct...but to me the degree of difference that might make it a better comparison is if his best buddy was involved with helping the tobacco company hide or change info showing cancer links.
Recusal would seem logical if not demanded.
as for private religious school cases, I'd agree up to the point of the school(s) being his or his kids' schools involved in a case, or if the school(s) involved were under the same "Corporate" Church control (I didn't know what to call the quasi business structure or if Archdiocese is too broad).
His wife didn't ring doorbells and hand out leaflets. She was in direct and strong contact with one of the POTUS' top guns and more. She may not be on trial but she might be like the buddy helping hide cancer research...?
Does that make any difference to you?
I see your distinctions and understand the nuanced differences you are pointing out. Hypotheticals suck because they never actually match the current circumstance adequatly. I think they all fall within the realm of involvement/culpability/knowledge on the part of the Justice. If someone shows me text messages or emails between Justice Thomas and his wife (or some third party) where Thomas is encouraging, participating, approving or having some level of involvement, then damn the torpedos he needs to go. Being married to someone with differing views, even subversive ones if you like to categorize them that way) doesn't mean that Thomas himself believes or is influenced by those same ideas. As a matter of fact, he may abhor her viewpoint/ideas, but the sex is so good he sticks around anyway.
My point being, I think there are (at least) three levels on the scale:
1. Possibility of impropriety
2. Appearance of impropriety
3. Evidence of impropriety
In my oppinion, we are at level one. If someone shines light on info that advances my perception to level 2 or three, I think this dog may hunt, but barring that, I recoil at the notion of passing judgement based on innuendo, association or supposition. Show me the email/text where Ginny flat out tells Sydney Powel that she "has the full backing of her Big Guy..."