Recognizing that not every antiquarian archaeophile need be an actual neophobe, nor must all neophobes be limited to matters of language, a more targeted term would seem to be in order. That’s because an unqualified term like purist or traditionalist wouldn’t be quite up to the job requirements unless it were prefixed with something like language or linguistic.
Now if it were me needing to come up with a term for this, I’d happily join together more than one word, each reasonably basic, to create an unambiguous term.
You have three possible ways of doing that join operation, but how you do that is up to you.
If you use spaces to join these multiple words into a compound, nobody will be scared away from them. Simpler terms like language primitivists for people forever mired in atavism like an ancient fly in yesteryear’s amber, may or may not be easily understood. This is the approach I would use, since it is always going to be clearer than runningeverythingtogethercaneverbe.
If instead of spaces you use hyphens to chain these separate qualifiying or limiting words together, then some folks might be a bit put off by the glosso-labio-laryngeal
catenativist concoctures that might ensue. So let’s not go down that route.
That leaves you with the third way of making compound words: if you use nothing at all to glue your words together, electing instead for the so-called “German approach” so beloved of otorhinolaryngologists, then any number of possible terms suggest themselves — but might not be immediately apprehended by the casual listener.
Just as a musophobist is someone who regards poetry with a suspicious dislike, one can readily neologue any number of sesquipedalian terms for these stick-in-the-muds1 who feel the same way about novelties in language, of which a neolinguaphobist is just the most obvious.
The appealingly amusing thing about that particular choice is that such linguistic fossils as you describe would surely despise having a word like neolinguaphobist minted on demand and waved menacingly in their general direction. :)
1. Or is that sticks-in-the-mud? :)