At what price is one considered an Audiophile.

For the term AUDIOPHILE, I'd say the BIGGER spending you have, the BIGGER audiophile you are. Audiophiles are the crowd educated by market and salesmen more than by experience or educational books.

For audio hobbyists it is not necessary to that magnitude due to the larger education and experience scale. The LARGER this scale grows, the lower money you need to spend on audio per given quality. 

For me, all I need is my speakers to sound as close as possible to my accordion, piano and guitars. Nothing less and nothing more.

+1 @nonoise re: your soul.

“I refuse to join any club that would have me as a member.” Groucho Marx

An “audiophile” only need be self proclaimed. 

$0. You are an audiophile if you love music, sounds, and notice and appreciate all the nuances you can experience in listening.  Steve Gutenberg knew he was an "audiophile" when he'd spend time just listening to the various qualities of hiss between FM stations. 

Money and equipment are the means to let us experience that which we love, but it doesn't make you an audiophile.  

Audiophile. It's largely an ambiguous term.

Do you like music?

Does what you listen to it through sound good enough to you?

If not, are you improving your equipment enough so that you do like it?

Good enough. Except for helpful advice, nobody else's opinion carries much weight.