In normal usage, I think the word is "traditionalist".
"Paleophile" would be a better word but I don't find it in any dictionary: it's not an accepted word.
- Very late addition and clarification *
If there is no well-known word that expresses an idea you want, you can, of course, always make up a word or use a word that somebody else made up and that only 10 people in the world know. But then you can't expect your readers to know what it means. You'd have to define it. Don't make up a word or use an obscure word with no explanation.
If you would only use this word once or twice, I'd say, in general, don't. Just use a phrase to explain what you mean. If you need to use the word many times so that using the same phrase over and over would be awkward, then sure, invent a new word, define it, and then use it.
Like, "These people are what I will call 'paleophiles', by which I mean, people who love old or ancient things. Paleophiles often ..." etc.
Best Answer
I think exhibitionist may fit your description:
and grandstander (also used in a figurative way)