One of the most serious problems with religion is how often and easily it can tend towards or support authoritarian movements. This is something irreligious atheists frequently criticize about religion, so perhaps it should be expected for religious theists to try to turn this back around and accuse their critics of being authoritarian as well. In doing so, however, they not only misrepresent atheists and atheism but completely distort the nature of authoritarianism itself.
An authoritarian is someone who favors "complete obedience or subjection to authority as opposed to individual freedom" and authoritarianism is a political or social principle in which "individual freedom is held as completely subordinate to the power or authority of the state, centered either in one person or a small group that is not constitutionally accountable to the people." According to some religious theists, there exist fundamentalist atheists who are authoritarians because they insist on using the scientific method for studying and evaluating religion.
Where is the denial of individual freedom in this? Where is the subordination of individual's will to the state or to any outside organization, if we are generous and define the concept more broadly? Where is the effort by atheists here to exercise "complete or almost complete control over the will of another or of others"? Nowhere none of the definitions of "authoritarian," however broadly conceived, apply to what is claimed about the behavior of atheists.
The claim itself is generally made in a false and unsupported manner. Religious theists are likely to say that atheists want to subordinate all aspects of human life to science: religion, art, poetry, love, etc. That's rarely, if ever, true. It would be unusual to find an atheist who says that science answers "every human question." Instead, an atheist is more likely to respond that science is the appropriate tool and the scientific method is the appropriate method for answering our empirical questions about what is and is not true about the world around us. This includes empirical claims made in the context of religions.
Every day we are faced with a bewildering array of claims about what is and is not true: political claims, social claims, commercial claims in advertising, personal claims, and of course religious claims. We need some way for differentiating between those that are most likely true and those that are unlikely to be true. We rarely have much time to make a fully reasoned decision, so we often have to employ quick heuristics and then just get on with life, but we have to recognize that this is far from ideal. When it comes to something really important and serious, we need to use the best methods available to us and those methods are part of the scientific process.
It's not a coincidence that science has provided us with so much consistently true and reliable information about our world in such a relatively short period of time. Science isn't perfect, but it works and it works more consistently and reliably than any other method thus far devised. This is not to say, however, that science always has much to say about things like art and poetry. It does have some things to say about how art works on the human brain, for example, but some aspects the arts also aren't touched upon by science.
I suspect that religious theists who make this false complaint are likely among those who also view religion as being something akin to art a system that isn't "true" in the literal sense, but is still somehow "true" in a metaphorical and spiritual sense. The problem is, traditional religion is not treated in this way and does not make it's claims in this way. Religion makes very specific claims about the world around us and religious believers generally accept these claims as true. So long as religion makes empirical claims, it's subject to the same empirical scrutiny as anything else which science deals with.
Atheists who evaluate religion and religious claims on the basis of the scientific method are not "authoritarians" because they are not trying to exercise personal control over others, nor are they trying to have science exercise control over others. Atheist critics of religion use science because that's the best method for differentiating true from false empirical beliefs. Atheists are using the same methodology as people should and do use in most contexts for trying to determine what is and is not true.