Question: Is it so that respect must be earned, not given freely?
Answer: If a total stranger is rude to you, what will you do?
Question: Tolerate and keep quiet to avoid friction.
Answer: Is that being respectful?
Question: There is no choice as peace and harmony is important.
Answer: Did that person earn your respect? Or was your respect given freely? Did you already answer your own question?
Question: Kind of.
Answer: Being respectful is right, but you should also say or do whatever else is needed, if appropriate, as a response. (Sometimes, not having a response is more skilful.)
The fact that all sentient beings have Buddha-nature (佛性: the potential to be Buddhas) means there must be universal respect for them, although we do not have to respect any of their unethical behaviour. It is with this fundamental respect that we try to correct them whenever possible.