I think that they both have points...
I think that only Tina
has a point.
Tom is an utter bacon-fed knave.
You could tell him that. Well, no, not really, but you could stop thinking of him as "having a point," and instead simply say, "yeah, I know, Tom, it really sucks to have [celiac/whatever]. I can't imagine how frustrated and angry that must make you at times. But Tina isn't your enemy, and if you can't handle the emotions, you'll need to stay home. Because you don't have a point. You're just wrong."
The *only* thing Tina has done wrong at all is to even argue (she's a perfect candidate for the advice, "don't JADE"). She's generous to go get Tom a gluten-free cupcake (or whatever it is), what a nice lady!
Now she should simply be amused at him. Frankly, he's laughable.
But basically Tina should simply refuse to speak of the topic anymore (as should you), with anyone--but especially with Tom.
There's nothing more to talk about. And anyone who brings it up should be told: "I am not having conversations on this. If you are going to persist in talking about it in ANY way, I am going to have to un-invite you."
In fact, it's time for her to call Tom and say, "Listen--are you going to be able to be pleasant company at my birthday party? Will you be able to keep your mouth shut about the cake? Because if not, then I'm afraid I'll have to un-invite you."
Tom is an utter, complete, and total boor.
And Tina is totally, completely and utterly entitled to call him "a big baby" and to speak of him in whatever scornful tone she wants.
And if you don't want to hear her talk about him that way, maybe you should be saying, "Let's just not talk about this anymore--put it out of your mind. Let's talk about something else, because this conversation is unpleasant."
I did once have my mom tell me that I needed to be aware of how my resentment of someone was changing my personality for the worse--and that since my roommate tat the time was the one creating all the angst for me, I needed to either resolve things with her, or kick her out.
That's something a friend could mention to Tina: "You're letting Tom turn you into a snarky, ungenerous person. He's wrong, of course he's wrong--but when you fixate on him, I hear a tone of voice from you that's totally at odds with who you are really. Can you find a way to mentally move on from him? Even if it means you dis-invite him from the party."
And if she disinvites you, do your part to play down the drama. "Yes, well, Tom wasn't going to enjoy the party, because he's still really struggling with the adjustment of changing his diet so firmly."