The word "anti-Mormon" is what's called a "thought-terminating cliché," or in other words, an Orwellian "newspeak" term. The purposeful use of a word like this is a subtle brainwashing (or "conditioning," if "brainwashing" is too strong of an expression) technique. By arbitrarily branding all so-called "opponents" with a word specifically designed to create a mental aversion, the leadership of an organization cues their membership to subconsciously censor themselves every time they use the word. This is a common tactic employed by authoritarian organizations which seek to reduce the flow of information to their followers.
The fact, however, is that extraordinary claims require extraordinary evidence. This is all the more so with claims as extraordinary as Mormonism's. If the evidence is not enough to verify the claim, some people are naturally going to draw a different conclusion. After this, some of these people are going to feel obliged to relate their interpretation of the evidence in order to offer a balanced viewpoint. For example, Christopher Columbus wasn't attacking anyone when he claimed that the earth was round, he was simply giving his analysis of the data available to him. So instead of turning and running every time the word "anti-Mormon" is used, Latter-day Saints should react and respond directly to the various issues and viewpoints they encounter. After all, the truth can always withstand scrutiny.
If you still believe that objectively studying your faith from all angles is somehow a bad thing, then here are some quotes from prior LDS leaders on this topic:
"If a faith will not bear to be investigated; if its preachers and professors are afraid to have it examined, their foundation must be very weak."--Apostle George A. Smith, Journal of Discourses, Volume 14, Page 216
"I think a full, free talk is frequently of great use; we want nothing secret nor underhanded, and for one I want no association with things that cannot be talked about and will not bear investigation."--President John Taylor, Journal of Discourses, Volume 20, Page 264
"Convince us of our errors of doctrine, if we have any, by reason, by logical arguments, or by the word of God, and we will be ever grateful for the information, and you will ever have the pleasing reflection that you have been instruments in the hands of God of redeeming your fellow beings from the darkness which you may see enveloping their minds."--Apostle Orson Pratt, The Seer, Page 15