The thing that Rovelli is arguing against (well -- not really arguing -- more, "stubbornly sticking his head in the sand" against) is not really a position that is held by a bunch of religious people trying to create a weird "god-of-the-gaps style argument" as you characterize.
Like, that may have been your experience -- not contradicting you on who you've met and what you've talked with them about etc. ... but what he's talking about is a position argued by a lot of philosophers and including those who have no particular metaphysical commitments.
Rovelli here does a lot worse than Dennett's "quining qualia" paper where he tries to get people to be really specific about "what are these qualia like" and finds that they're so hard to embed in language, to symbolically represent, that maybe he-as-philosopher can discharge his duty to be engaged-with-phenomenalism by just kinda sticking his fingers in his ears and saying "what phenomena?! you haven't clearly defined the phenomena!"
But someone like Searle who has no bones about himself being an atheist and, while he didn't like to describe himself as "materialist" because of the history of that term[1] he would acknowledge that it was close to his basic position. And I want to be clear that he views consciousness as a scientifically solvable problem. He doesn't think we've solved it yet but he thinks the philosophical problems are ultimately tractable and if we solve them and get out of the way you'll get a fine science of consciousness someday. Nevertheless, he's very clear about agreeing with the fact that these qualia are important to the discussion and he would laugh at you for trying to leave them out -- he'd say, now you're trying to make a science of consciousness, by leaving out the consciousness. And of course you don't think there's any science left to be done at that point and "well, it's all deterministic physics, we understand it all, nothing to be done here."
So like if you want to read his take, a book is Freedom and Neurobiology, but for this comment I just want to point out that him simultaneously believing that there are phenomena of experience, and believing that there is no God, are two beliefs that are not uncommon for philosophers to hold together.
1. There's kind of no way to very briefly make the point since you kind of need to be hit in the face with a sledgehammer about it. So Searle views Descartes as erroneously trying to package up the world into two realms -- mind properties or substances on this hand, physical properties or substances on that hand -- and insisting that they can't overlap. And then Descartes' legacy was that you had camps which said 'those mind properties aren't real, only the physical properties' (materialism) and 'those physical properties aren't real, only the mind properties' (idealism) but coming from the same mistaken beginning. Searle would point to the score of a football game and say 'now is that physical because it's represented in terms of lights on the scoreboard, or is it mental because it's represented in terms of the thoughts of the referee, what about all the people on both sides who think the referee made the wrong decision -- something which, remember, by definition the actual referee cannot do; they are the final authority -- and they believe that the score is "really" some other number distinct from the score represented on the lights; and what if none of these people are "right" in the sense that if a perfectly perceptive model referee could have made all of the scoring calls in the game according to the rules on the books, then the score would have actually included an event that everyone watching thought was unambiguously non-scoring but actually it was completely legal and valid. But here I-the-philosopher come into all of this absolute mess and I want to carve out a clear boolean yes/no classification, mental vs physical, material vs ideal, which is it -- the problem, was not that I counted to two distinct possibilities, but that I thought counting those possibilities was a meaningful way to decompose the problem in the first place.