Isn't it that even when we use the Scientific Method, the difference of opinions/conflicts still exist, right, please?
The scientific method allows for a method to resolve disagreements.
1. Find/design an experiment that will give one result if one person is correct and a different result if the other person is correct. If no such experiment exists even in theory, then there is no *actual* disagreement.
2. Do the experiment and see what happens.
3. At the very least, if steps 1 and 2 are done properly, at least one person will be shown to be wrong. That person needs to modify their beliefs to agree with the results found.
Differences of opinion can persist if we cannot, for some reason, actually perform the experiment (say, we need funding to build the apparatus to conduct the experiment) or if we didn't design it appropriately, so it gives ambiguous results. If we don't manage to do a conclusive experiment because steps 1 and 2 are not currently possible, then disagreements can continue.
But, if the experiment is properly designed (by both/all sides), then actually doing the experiment should at least say at least one person is wrong.