At what price is one considered an Audiophile.

Then: ARC SP-11, D-250 servo, Acoustat 2+2 med, full blown Linn and quite a few high priced peripheral equipment. Total then about $40g Can.
Now: Marantz 1040, Mission speakers, Technics 1400 Mk2, Shure M97x. All used except cartridge. Total: $750 Can. including NAD cd and old iPhone. It sounds great!
After 35 years or so I just lost interest in the “hobby” and in the endless spending. But not in the music.

Still an Audiophile … Don’t need extravagant set ups to enjoy music. 

Dignity 

Buying great audio equipment is the easy part. Getting my hearing that I had when I was a young man is impossible.

@carlsbad2 has a point here... I have a friend who asked me to spec out an audiophile-grade vinyl system for at/under $1k.... I thought I could do it, but it's really not possible. I've found that I need at least ~$1.6k ($400 for a decent turntable with something like an Ortofon 2M red, $400 for a decent amp/avr, $500 for decent bookshelf speakers and stands, and $300 for rack, surge protector, and basic cables) to get to a very entry-level "audiophile setup." while there are plenty of people that wouuold turn their noses up at a system like this, with the proper acoustic treatments and room positioning, a system like this could sound pretty good.

I think there are plenty of audiophiles that are super interested and enthusiastic about audio reproduction, but aren't ready to spend the kind of money it takes to unlock true hifi sound. So I guess your question breaks down like this: anyone can be an audiophile, but an "entry-level, audiophile-grade system" will cost you ~$1.6k-$2k.

Finally, as @designsfx points out, just because someone spends a lot on a system, that doesn't automatically make them an audiophile. Thoughtlessly throwing money at gear is the antithesis of what this hobby is all about in the first place!!!