I think similarly. Though my thought as to why the Prophets did the whole "we don't understand linear time" act is that it was to get Sisko over his survivor guilt. I believe the episode really turned on the lines about Sisko still living in the moment he left Jennifer on the Saratoga and how that wasn't linear.
Well, not exactly. A few are declared "not god". Most are simply not declared "god", which is quite different. As far as we can tell, our heroes might accept gods as a specific category of beings out there, without being unduly excited about it. OTOH, at times a vehement "not god!" statement seemed to be in downright error. Apollo very definitely was a god, more specifically the god named Apollo - this much the heroes accepted as in-universe solid fact. They just for some reason rebelled against applying the historically accurate label, moving the goalposts to meet some sort of religious agenda of theirs. I mean, what's the point of the semantic dodge? When suddenly meeting a temporally displaced Edward VIII, would they similarly declare him "not king!" on the same rationale that mankind has outgrown its need for kings? Timo Saloniemi
The Enterprise crew did not dispute that Apollo was the god of Greek myth. But the monotheistic religions only use the word god to mean an all-powerful, all-knowing being, which neither Apollo in TOS episode nor the Greek gods in myths were. They were flawed, capable of being taken by surprise, subject to human weaknesses. I don't think Star Trek is ready to deny the monotheistic god. For one thing, they need to be aired by TV stations in the Bible Belt. They'd much rather just not say anything either way about the monotheistic god, anything they say would get them into trouble somewhere.