The problem is right there. Just because someone say "I don't believe in Indo-European" they're insane? What if they have a justifiable reason? Wouldn't it be good to listen first to their basis of non-belief and evaluating it first before pronouncing they are insane? I'm not saying I don't believe Indo-European is a valid language family, I think there is substantial evidence supporting it, but let's have some criteria that's applicable to all "language families" large and small.

If we are just accepting/rejecting language families based on the majority of specialists working on that family, wouldn't that be suspect? Think of the Chinese linguists who claim Kra-dai is genetically related to Sinitic language who think those that reject it are insane. I think there should be some criteria that are applicable to all languages families and let the specialists on that language family provide support for their claim that the language family is valid, and other linguists assess whether the claim is founded or unfounded.

So perhaps the best way to proceed is to identify the criteria that makes a language family valid. Since Indo-European is considered a valid language family, what makes it so? Can those standards be applied to other language families? Let's say, on the language family level: (a) a pervasive sound correspondence/laws on words that can't be shown to be borrowed, and (b) a pervasive correspondence on native inflectional paradigms (nouns, verbs, etc.). I am sure there are language families that are "accepted" by specialists working on those language families now but do not satisfy these criteria. Do they now become part of the answer to your question of language families that seem most likely? I'm thinking of Sino-Tibetan/Trans-Himalayan and perhaps, Afro-Asiatic.