Being polite is always about appearance. Politeness is important here for all the same reasons we raise our children to be polite to others. It is definitely not weird.
Disagreeing politely is not impolite, and providing counter arguments politely is not impolite. Either you are polite or you are not.
There is a difference in how contrarian you can be in a discussion, depending on how well you know the other party / parties. The extra context provided by knowing people well allows for more freedom in the discussions, and modifies what is considered polite.