Some religions are not only false - they are indeed without truth conditions. Not all, but when you talk about an ““unkowable god”, or “The deep-essence of everything loves is”, that lacks any truth condition. So, even if it is false, it is false in another way than “Doug is a woman”.
Actually, I would agree with you there. There are some sorts of obscurantist beliefs about religion (or indeed some ideas coming from postmodernism) that do seem to me literally nonsensical. This is a sort of jujitsu tactic of those on the losing ends of arguments sometimes. They basically blow smoke.
But I’d argue that sort of tactic is in the minority, except perhaps in some of the so-called “sophisticated” sorts of theology.
“there is a transcendent being” is a statement without a truth condition, and that is not sophisticated theology. I cannot think of a state of reality that would falsify it. Again, it is very unlike “G.W. Bush is a lake”. Do you think that saying “a transcendent being” has sense? In what category would you put it? For me sense is related to verifiability.