Interesting topic.
I like this definition that I found online, where "fetish" refers to "a strong sexual preoccupation with an object, material or body part." Examples might include: a shoe fetish, a latex fetish or a foot fetish. The fetishist almost literally needs those things in place to get off sexually.
I would go one step further to say that fetishism is extremely specific. Even a foot fetishist might prefer women of a certain ethnicity, with a foot size/shape range from "this" to "that", toes shaped in a particular way, wearing a specific type of shoe, having either washed -- or not washed -- her feet for a predetermined length of time. As they say, the devil is in the details.
How TER uses "fetish" seems to be code for kink-friendly, instead of the actual meaning, but what you said about an open-minded and nonjudgmental attitude is really all clients are seeking. The sad thing is that so many of us think that we are freaks of nature when our kinks and fetishes are (relatively) common . . . or, at least, not that uncommon.
My interpretation of fetish-friendly if it was used in the correct manner would be that the provider is willing to engage in a certain activity during the session in order to please the client.
The thing about fetishists is that they tend to pre-fantasize in exacting detail, and anything that goes "off script" is going to disappoint them, so it is in the provider's best interest to understand what that "script" in the fetishist's head is and try to hit those specific marks