What does the phrase "anti-Christian bigotry" mean?
In general, I think the word bigot is overused. For instance, even though I do think that some people who oppose marriage equality are anti-gay bigots who really do not like gay people, I do not think that all people who oppose marriage equality and other LGBT rights are. Oftentimes, on any side of an issue, the label bigot is used to dismiss any opposition, rather than to deal with actual arguments people are making.
Generally, when someone calls another person a bigot, he or she means something along the lines of someone with a prejudice or intolerance of people with certain fixed characteristics- things like race, ethnicity, sex, sexual orientation. What is becoming ever more common in this day of the Christian Persecution Complex, is that some have co-opted the bigot label and are now applying it to people who display prejudice, intolerance, and even mere disagreement with another person's religious beliefs. Yet, given that one's religion is not an inherent part of oneself, what does it actually mean to be, for instance, an anti-Christian bigot?
For some insight on this matter, I visited the website of the Christian Anti-Defamation Commission. The closest I got to a definition was a plea to make a "suggested donation" for a book all about the topic. Not very helpful.
Seeking a less expensive answer, I turned to the dictionary. Dictionaries generally define bigot as something along the lines of "a person obstinately or intolerantly devoted to his or her own opinions and prejudices" or "one who is strongly partial to one's own group, religion, race, or politics and is intolerant of those who differ." An anti-Christian bigot, then, would be one who is stubbornly devoted to one's own religious opinions and/or who is intolerant of those who differ.
The first part of this definition, one who "is stubbornly devoted to one's own religious opinions," I think would be true of most religious folks. In fact, such devotion is often a hallmark feature of what it means to be a "good" person of faith in many religious traditions. Atheists, too, are even stubbornly devoted to their opinions regarding god's absence.
So, I think the real test of bigotry is in the second part of the definition: one "who is intolerant of those who differ [with respect to their religious beliefs]." It is important to distinguish between tolerating another's beliefs versus tolerating that person's humanity. I know that critics of religion in general, and of Christianity in particular, can be harsh, just as critics of atheism, agnosticism, and secular humanism can be. Oftentimes, criticism goes beyond criticizing beliefs and into the realm of personal attacks. Yet, I do think it's important for people to remember that criticism of another's beliefs, opinions, and arguments is not, by itself, intolerance or bigotry. That is a very important distinction that Christians often muddle and abuse.
We are all free to criticize and reject other people's religious beliefs. So, claiming that critics of Christianity are automatically anti-Christian bigots is like accusing Democrats of being anti-Republican bigots. In other words, yes, many people disagree with the various tenets of Christianity, but so what? Disagreement does not equal hatred of another's humanity. I know that some people do hate Christians, and it's often an unfortunate reaction to Christian intolerance, but in general I think many politically-active conservative Christians are too quick to label any sort of criticism bigotry. Just something to watch out for and be aware of.