(Liberal) Implicit Egotism Fallacy or Bias and Islam

I was talking recently to a fellow liberal who happened to be a Hindu making correctly scathing attacks on UKIP (a right-wing pseudo-libertarian UK political party similar in many ways to the Tea Party), media bias and misrepresentation and, you guessed it, Islam. Again I was somewhat frustrated that an intelligent and informed guy was getting so much right and yet made one big error. I see it so often and have been involved in debating it here and here that I had to answer my critics here. The problem is so common that I am formally going to name it as a fallacy or bias (though no doubt it already exists and you readers will tell me).
In simple terms it goes like this:

I am a liberal and I much more appreciate the liberal and moderate Muslims, and I don't like it when fundamentalists are used to represent Islam. As a progressive liberal, I better associate myself with liberal Muslims and therefore think that they better represent Islam than fundamentalists.
I could call this the liberal Implicit Egotism fallacy or bias, but in more general terms it could be called the Implicit Egotism Fallacy or Fallacy of Implicit Egotism. I have talked about implicit egotism before: it is where people look in others for traits about themselves and thus end up favouring the others who better reflect themselves. In this case, people with liberal persuasions better align themselves with those in the subject group who reflect those persuasions. For example, the other day, on BBC Radio 5Live, Adrian Chiles was interviewing two liberal Muslims who worked in the field of dealing with and working against Islamic extremism in the community. This was in response to a raft of new proposed legislation for anti-terrorism in the UK by Cameron's Conservative government. Chiles said the give-away phrase, "Of course, not all Muslims hold to the genuine peace-loving Islam that you do". Chiles, here, automatically, and without much question, took on the liberal "peace-loving" Islam as being the correct "genuine" one. Who gets to decide that? Is such peace-lovingness actually borne out in the holy texts? I would argue not. Whether it is or not is not so relevant here. The idea is that Chiles projected his own peace-loving morally progressive worldview onto others, or sought out his own worldview in others, such that they became representative of the "genuine" Islam.
And this happens day in, day out. This is how it looks as a syllogism of sorts:

1. I have traits A
2. I morally evaluate a group of people X which includes people with traits A, B, and C
3. Associating with those with traits A, and implicitly due to this, I come to take them as properly representing X

Yes, the (UK) Daily Mail and other right-wing rags do misrepresent Islam on account of their inherent biases and closet racism and otherisation. However, this does not mean, by default, that Islamic liberals are the more correct form of Islam. I have expressed this at length elsewhere as linked above. The main point is that we should question our approaches to other groups of people especially when it appears that we are merely seeking reflection of ourselves.