They are incorrect on two points. First of all they regard Atheism as a life style, which it is not. Atheism simply means that it rejects the existence of a God. Nothing more. There are conservative Atheists, socialist Atheists and so on. Life style has nothing to do with it. Secondly comparing Atheism with religion is a “Fallacy of Association” (red herring) which states that the quality of one is comparable to the quality of another by an irrelevant association. Atheism is not comparable to a religion because they are not associated.
Religion vs non-religion is an opinion, not an association. You cannot say that ”non-religion” is a “religion”, just like you cannot say that “non-belief” is a “belief“, ”non writing” is “writing” or “no money” is “money”. You are either religious or you are not. That’s the choice, that’s an opinion. Now if you are religious you can be a member of thousands of religions and you can believe that yours is the only correct one. If you are non-religious, you have rejected all of them. If ”non-religion” was part of the list of religions and you reject all of them you would be rejecting your own ”non-religion” religion, a contradictory statement. This is called “an inductive informal fallacy of association”.
Conclusion, religious people cannot logically call non-religion a religion and then use that to bolster their argument. It is an OPINION. When you are religious, you have an opinion and then secondary you “believe” that one of them is correct.