I fully agree but the point is that they themselves label as a moderate or a conservative just to hide themselves for the Western Audience. So when a person labels him or herself as a moderate then surely i can address her or him as a moderate wouldn't you agree?
In my opinion and i will give a little example: some moderate Muslims who don't allow Sharia to take place or is firmly against it then that person is not a Muslim (In my eyes). since its a obligation and a creed in Islam to belief in god's law and carrying it out, this doesn't mean who ever disobeys a Sharia-Law therefore is not a Muslim off-course, but who ever is against it.
So while agreeing with you, don't you think that these people who label themselves are the ones who make themselves victims. I think the term Moderate is never used by other Muslims to insult others but to clarify what the difference is since the moderate themselves use the term to label there different ideas and customs.
People labeling themselves 'X' is one thing; other people using labels such as 'X' and throwing them around as means of stigmatization is quite another.
I personally think that it's way above my paygrade to judge who is a Muslim and who isn't, particularly because different people have different views when it comes to what falls under the umbrella of Sharia. Looking at many countries' laws that supposedly follow "God's law" (such as Morocco, where a girl was forced to marry her rapist and consequently committed suicide earlier this year), I think there are very good reasons as to why many people would be opposed to the idea of someone carrying the ball of implementing religious laws into constitution.
That's not to say that I'm against Islamic laws; I'm not against them at all, but I understand why some people would be concerned with how religion can be used quite manipulatively to justify abuse -- like how the case was with Amina Filali and others.
If a word is used differently by different people, it doesn't mean it is meaningless, it just means there is a disagreement on the term. The idea isn't to label or judge, but to understand whether there is anything in Islam that is conclusive and authoritative. If most of the scholastics/Imams interpret the Quran in such a way that does not describe most Muslims in America, then it's normal to ask why that is.
Authoritative sources go beyond culture.
Asking "Why?" is completely different than judging people of the same religion according to their stances on certain issues, or declaring them outright disbelievers.