Philosophy welcomes anyone, as well as science. Being a professional philosopher matters to the extent that other people's opinions matter. What you describe about old philosophers and mountains, is what I do whenever I pick up a book! I can go back 2000 years ago, or travel to another continent, etc. I would listen to anything your non-specialized philosopher has to say. After all, I read a lot, and reading is by its nature mostly listening.

I actually get your comment quite often in different forms, I mean the gist of it, which I believe to be "can't non-philosophers philosophize?" or "aren't we all philosophers?"

The thing is, practically, you can discover all the truths of mathematics by yourself, but you'll benefit if you study others who went over it already. It will save you time, and keep you from "wasting" your time rediscovering other people's thoughts. If I were an immortal I'd rather rediscover it all by myself, but we don't have that luxury of time, so we must cut corners, i.e. study, either in an academic institution or independently but with similar rigorousness.

In general, I would learn from anyone, and we should all learn from everyone. Sometimes though people are just inconsistent. There are rules of thought just as there are rules of math. Sometimes people are even downright mischievous and dishonest. We should recognize those cases, so as to release ourselves from the tutelage and/or influence of these people as quickly as possible!

As always, I'm thankful for the reading and the comment, hopefully my reply is up to par!