I think most atheists respond with the most venom about theism when they are proselyted or when they have rules imposed on them for theistic reasons. In Alabama that likely means all their full power screeds against theism are going to seem Christian specific. In Turkey they are going to seem Islam specific.
A presupposition of the question that started this thread is that all atheists are of a single mind. I think the group of people who identify as atheists are likely to have some things in common more often than theists, but only a little bit. Individual atheist organizations have positions and stances, but atheism does not represent some sort of hive mind.
But back to Christianity as more criticized by atheist than other religious groups, I can only really talk about the US. In the US there are over 2,000 Christian radio stations. If you are in a major TV market I bet there are a few Christian broadcast TV stations. No selection of cable TV or satellite is going to come without some evangelically oriented stations and EWTN for Catholics. Yet ever slightly critical sentiment expressed about Christians gets portrayed in Christian media and on Fox news as a wave of intolerance or a new persecution. I know there is real persecution in parts of the world. Not letting someone evangelize on the court house stairs or read from the bible in a high school commencement address is not persecution like people in Syria or Nigeria experience.
I think in BL terminology a lot of the perception that Christians are more criticized ought to be considered as likely being about the fact that Christians are most apt to have major butthurt about any sort of commentary. Xians demand a lot more deference from commentators in the US and in American fashion they get the same Bronx salute other demanders get. I do have anxiety about how muslims will be when they are less of a minority. For know though Christians are a large percentage of the population with considerable influence. Attempts to curtail critics by claiming they are unfairly targeted or persecuted are mostly ridiculous. Sorry for the butthurt, perhaps some salve and a comfy cushion.