The existing policy
Working purely off of existing Stack Exchange policy, I'd like to reference Pops's answer to As a moderator, how do I handle a potentially inappropriate profile picture?:
Avatars are much more visible as we show them under every single post that you write, and as such, are open to a tad more scrutiny. If the avatar:
- Depicts or promotes hate in any form
- Insults, is insulting to or negatively objectifies those belonging to a certain race, gender or religion
- Otherwise creates disruptions that moderators must deal with
... then we're probably going to require you to use another avatar.
Try to be as tolerant as you can of other people, and assume good intentions until you have evidence to the contrary. "It offended me" is much different from "might offend someone", so don't go out of your way to flag something unless you truly believe it's a problem that requires immediate intervention.
The latter point is something I think we can all agree upon. Don't assume that other people will be offended by something. For example, my cross country team was previously prohibited from running in a meet on Yom Kippur because the school administration feared that Jewish runners on the team (and their families) would be offended. As it turned out, every Jewish runner on the team had previously talked with our coach and decided to run on that day. Regardless, however, the team did not go to the meet. This was a case of someone acting for someone else, and it was, in everyone but the administration's opinion, a mistake.
Under existing Stack Exchange policy, phobias would fall into the third category, if they can be shown to be disruptive.
Pops' answer creates three separate categories that encompass everything (two major ones, and a catch-all one). Avatars creating phobias may fall into the first two categories, in which case they would be changed. However, the point of contention here is whether or not other avatars that aren't in the first two categories cause disruptions - and whether or not that affects someone's freedom of expression (see Deerhunter's comment).
Clearly, freedom of expression and freedom of speech are nullified in certain conditions:
However, these conditions are not necessarily met here.
Avatars are examples of expression. I choose to express my nerdiness via an xkcd character, Black Hat Guy. However, if Black Hat Guy went around calling people morons and spewing hate speech, then it would no longer be an appropriate avatar. It would be offensive.
In this case, does fear trump freedom of expression? I don't think it's right that one person should be beholden to curb their freedom because one other person is offended. If I'm afraid of disembodied heads, then that really shouldn't stop Shog9 from having his profile picture be
his a disembodied head. It's not fair. Just because one person isn't happy about something doesn't always mean that another person should change. More than one - or two, or three - people should be affected negatively for an avatar to change, in my opinion.
You've argued that phobias can have serious consequences. Indeed, this may be the case. I have a terrible fear of closing my binder on my hand, thus impaling it (true fun fact; it's why I dislike filing papers). That doesn't, though, mean that it causes a serious disruption to my life. I'm not trying to trivialize phobias, but I am trying to say that most phobias are not seriously disruptive. Especially if only one person is disrupted for the short amount of time they have to view an avatar.
So, I would support taking action against an avatar that caused a phobia if
- It can be shown that more than a handful of people find it disruptive.
- It can be shown that the disruption caused by the avatar seriously impacts their lives and/or use of Stack Exchange.
Point 1 would be invalid - if the disruption is serious enough. For example, if an avatar causes one person to jump out a window, it should be changed. Period. However, if an avatar causes a person to get shivers down their spine, then perhaps the disruption is not serious enough.
The words "handful", "disruptive", and "seriously" are about as subjective as you can get. They'll vary. But they should determine the actions taken on a case-by-case basis.
But - as has been established many times before, including in Kate Gregory's answer - let's agree to not act based on assumptions.