Applying for posdtoc positions: is it okay to send out many applications? When applying for postdoc positions, one has the option to send out lots of applications, possibly get several offers, then choose the one that seems best.

Alternatively, the applicant could contact the research group that looks the most relevant or best suited for him, and focus on getting a position there.  If the feedback is not positive, then (and only then) move on to the next best choice.

I believe that in the USA it is accepted that people will shop around for positions, and not taking an offer is considered completely normal.  However, in some other places it is possible that if the applicant shows a lot of interest for a certain position, then gets an offer to be hired, and doesn't accept it anyway, it could be considered rude.

What is the usual or best way for applying in various countries?  I think it is very important to research this point to avoid any misunderstandings or bad feelings because of differences in attitudes towards the application process.
You should remember that universities are also looking at the resumes of many candidates for a given position. If it is not rude on their part to consider many applications and rejecting most of them, why will it be rude for a candidate to apply to many positions and reject some of them?

This is a many-to-many matching market between applicants and positions. You are trying to optimize your chances, they are trying to optimize their interest. If you look at it from this game theoretic perspective, you will not feel any qualm of conscience.