I think you are absolutely correct. Many famous scientists were and are deeply religious. Science as a methodology is antithetical to religious methodology. The only problem with this is that some people think it's a problem. Science attempts to make observations, build models and predict things based on those models. It tries to actively falsify its own models by checking whether new observations follow the predictions based on the models. Your choice of whether or not to believe in the reality of the models is still your choice. While unfair and out of context, I like to quote Einstein here: "God does not play dice with the universe". He didn't like quantum mechanics because it didn't sit well with his belief of how the universe worked. Similarly, after Michelson and Morely won the nobel prize for demonstrating that the speed of light was a constant, no matter what reference frame you were in, they spent the rest of their years trying to disprove it! They knew that the consequences of a constant speed of light was crazy physics as envisioned by Einstein and they didn't believe in that kind of universe. This happens all the time in science. We use our scientific models because they are useful, not because we believe in them as some kind of absolute truth. Granted, some people do believe that, but that belief is not science. The big takeaway is that it doesn't matter what you believe if you are using a scientific methodology. It is irrelevant -- you use what works, not what you believe.

Religion is a methodology of belief. I can't tell you the number of people I've met in my life who would curl up and shut out the world if they didn't believe in something more than they could measure or extrapolate form existing models. This is human nature, for better or for worse. Belief is necessary for most people -- even scientists (though, as I said, quite a few of them choose to believe their own models).

Like some people, I have a problem with many organised religions. Historically, religions have been very adept at using people's belief in order to liberate them from their money or their freedom (or even their lives!). However, I don't think religion, per se, is the problem. Like I said, people need to believe something and religions offer that service. It's just that having inserted themselves into that picture, people have a tendency to abuse their position (often with a considerable amount of internal justification, but I think it is abuse none-the-less). On the other hand, I've seen religious organisations do a world of good as well. This rallying force of belief is extremely strong. Even when countries have made religion illegal, they simply insert the state as the object of belief. This is because (IMHO) belief is necessary to the normal operation of human communities (and sometimes also because they want to abuse their populations ;-) ).

WRT the idea that traditional ideas may have useful applications for science, this is undeniable. But many traditional ideas are also just snake oil. The best methodology for telling the difference that I know of is science. Starting with the assumption that traditional ideas are likely to be beneficial, I think is a poor idea. However, so is starting with the assumption that traditional ideas are necessarily snake oil. If you have a question, make observations, build a model, make predictions, test those predictions with new observations. You might be wasting your time, but you might not. That's science. If you want to believe something and it makes you feel happy, then go for it. That's religion.