Not sure if I'm taking the bait but here goes.

Science is a set of processes where you take belief out of the equation. You can start with something akin, which when you have informed belief you have an hypothesis which you set out to prove. You don't hold that as truth and anything not falsifiable is not a valid hypothesis.

Science is not a religion, it's just a thing. Plenty of people need to belief to function and end up having (even a blind) faith in science, using it as a religion.

On your second point I'm with you on the last part though I think you are calling religions and believes things that are organized religion and religion.

Contemporary philosophy and sciences are different from religion in some aspects. One important aspect is that these academic fields rely on rational arguments, while religion today mostly relies on traditional beliefs and faith.

Let's say a philosopher is pondering the idea that direct experience is not necessary for knowledge. The only way to go and declare this publicly is to elaborate why, how, in a rational and rigorous manner. Most scientists work with objects that admit replicated experimentation, so they must do that, let's say in their case, to demonstrate that a rain frog only comes out with heavy rain, but not with light rain. In contrast to these two, a religious or spiritual person might give "arguments", but this argumentation is never to see if their belief resists examination, it is only to convince others of this belief that has been established as truth before everything else. In other words, philosophy and sciences examine their thesis (hypothesis, theory, etc.) and never assume they have the ultimate truth; on the contrary, they keep searching and exploring possibilities. Talking here about the disciplines and not the individuals who can be different from this from time to time (e.g., a dogmatic professor). Meanwhile, religion and spirituality do not have thesis or any beliefs that are susceptible to drastic change. They establish core beliefs or dogmas, and only later might try to prove them or not, depending if they find this exercise important.

Are they all ultimately unprovable statements? I guess so, but we should care how these statements come to be and how we justify them. To me, it makes an enormous difference.
I rather believe in climate change in which human action is definitely affecting the Earth (source: sciences) and the importance of stopping it as we seem to have a responsibility to others and to ourselves (source: ethics, a branch of philosophy), than to believe that there is a conspiracy to make us believe about climate change (source: perhaps imagination) and that we shouldn't do anything anyway because there is no reason to (source: ignorance or dogmatism, honestly).

I try to remain critical of rational disciplines too, but that's ironically done with more rationality. And here I do not mean "cold" and rigid pseudo logical analysis, but something that admits different approaches as long as they are solidly justified.

I guess it comes down to who we are. I simply cannot be convinced without this I explained. I cannot believe in religion or spiritual beliefs. I sometimes get short videos about people telling many different stories, about ghosts, ayahuasca trips where they talked to superior entities, gods and the way they know they're real, etc. How can I believe what they perceive is real? Mere "leap of faith"? And why choose one over the other? Just because I like a particular system or because it benefits me in some way? Sorry, too arbitrary even for me that I sometimes act impulsively and capriciously. As I said, I guess the way we are allows us to accept or to deny different ways to approach existence. This is me.

Thank you for reading my stupidly long comment.