Very probably, there seems to be more than one fallacy at play in the rationale I linked.
Paranthetically I have also seen theists often accuse atheists of being atheists, just so that they can do whatever they want. A similar core rationale here, that no one can genuinely disbelief in a deity without an ulterior motive, again another variant of the No True Scotsman is.
This one is definitely falsifiable though. As there would be evidence of increased immorality among atheists. Where theists and atheists are compared objectively on a level playing field, I have only seen research showing atheists to be at least as moral as theists. For example studies of the percentages both demographics make up in prison populations in the US for violent crimes like murder and rape, show atheists as under represented in comparison to the general population. Though of course there may well be other factors to consider as root causes behind the data. However it habitually does not support the theistic claim to moral ascendancy.
However the main focus here on the initial claim, can simply cite that it is unsupported by any objective evidence. I would add that I have never encountered an atheist who was in fact a theist, pretending they didn’t believe, just to mask anger at a deity.
I find the claim not just irrational, but highly dubious. Though it seems a popular red herring, that crops up quite regularly.