Even though it is sometimes awkward, I understand the desire and need for gender-neutral pronouns. However, it's more of a challenge to appreciate the chosen pronouns being independent of gender. The site explains that a person choosing to use "she" is not necessarily identifying as female, for example, and that gender is a private matter. 
An interesting post on the matter by a teacher -- 
Why asking everyone their preferred personal pronoun is not a good idea 
		 
I severely dislike getting asked in those types of contexts. I get asked at almost all medical appointments, barring Mazzoni's clinic, which makes no goddamn sense when I 
know the information has been updated everywhere else. At this point I'm pretty sure Penn & Jefferson have been using me to train their staff & students because they keep trotting them in and 
I'm tired of it. Nine times out of ten I don't even get asked if it'd alright. They started out asking - they don't anymore. They stopped asking years ago. Now I get "I'm Dr. ----- and 'these are the five interns (or the occasional colleague, the last one was a woman whose facial expression I was 
actually close enough to see and it looked like she was standing next to 4-days-in-the-summer-sun roadkill, and what a pleasant pinch of the face 
that was. Clearly didn't want to be there. White cane doesn't mean 
no vision, and boy do cis people let their expressions slide). And it's always phrased the same way, 'preferred', with many pairs of eyes peering at you as if the info 
isn't listed in the chart and hasn't already been clearly indicated in my medical file with the 
plethora of other possible deliberate presentational cues used by, oh, just about 
everybody.  
And it 
is clear in the records. It's been in there for years and years and years.  The next time I'm just gonna go around the room individually, starting with the students, and ask all their 'preferred pronouns'. I've already inquired whether my information was correct and if my pronoun was listed at the end of an appointment several times and gotten an "Oh, yes.", once complete with a very quick and rather unsurprising scuttle out of the room by the doctor after, since I'd waited to ask until the students had left (different appointment).  Seems odd to me that the majority of my medical appointments still involve cis people gawking at me and claiming 'Respect!'  Fuckers.