When one responds to Roman Catholic arguments, they are called Anti-Catholic.
When one responds to Rabbinical Jewish arguments, they are called Anti-Semites
When one refutes the lies of those who propound the falsehood that homosexuality as biblically good, they are called homophobes
When one raises a concern about Islam, they are called Islamophobes.
These are often the phrases used either to irrationally dismiss the arguments of an individual or it's an emotional response when one doesn't have an answer. (Or if an answer can be given but still tries to get an emotional response from the audience.)
But in all seriousness, there is a difference between doing a response to these groups on a particular issue and just being plain nasty.
There is hateful bigotry out there toward these people and I don't deny this, but not everyone is guilty of this.
If one responds to an argument presented by any of the groups above and even presents a thorough refutation to the points made, Is the person inciting hateful bigotry towards these individuals? No.
Hateful bigotry would be simply just having a detestation for them without recognizing that not all individuals in a group are exactly the same.
There are individuals who from a human perspective (I say this due to the fact man is depraved by nature) who just simply want to live out there lives, not hurt a single individual and even display acts of kindness and charity, but, there are people who give a bad name to some of these groups to be sure.
If I say someone is giving a group a bad name, Am I demonstrating hate toward that person? No, I am simply pointing out that there are rotten apples in every basket.
You get bad eggs in every group, it's a fact, but responding to the arguments of a particular group does not mean you are "Anti-Catholic" or "Anti-Semitic" or "Islamophobic" or "homophobic" or whatever you want to throw at someone to envoke a particular reaction from your audience.
The next time either me or another person is responding to a heretic group in a paper, ask yourself. Are we actually promoting "hate speech"? or getting both sides to think.