At what price is one considered an Audiophile.

It would depend on who is doing the 'considering'. I wouldn't worry about it too much and just enjoy yer tunes.... 

Cost may be irrelevant, in a sense, because it's a state of mind, but if you want a good sound, even if it is the first step, it will cost. $10k perhaps, one source, used equipment except cartridge. If your room is big it will be more. If you listen to large scale music it will be more. Well, for $5k it could be possible to find something listenable, but it would be below audiophile level.

Money spent means nothing. I have heard systems that carry a price of many times what I’ve spent and I wasn’t impressed. As with life there will always be someone with more than you have. It’s easy to determine how far you can go or how much you can comfortably afford. The real key is focusing on the basics first- speaker placement, listening position and room treatments. Then work your way forward with the gear as your experience and budget allows. Anyone who thinks they are an “Audiophile” because they’ve spent a certain level of money is an “Audiophool”.

In the current reality $10k is not much at all, so good sound is not very expensive.

Excellent sound is expensive. 

Yeah it’s about the sound. It can be bare speakers hung in trees powered by a car deck. If you say, "wow, that sounds cool", that’s it.  That's audiophilia.  Some people don't notice or care as much or at all. Fortunately, or unfortunately, we do.