A landlord may reject a prospective tenant's rental application for any reason or no reason, so long as it's not an improper reason. By "improper" I mean discriminating against a prospective tenant based on race, religion, nationality, family status, etc. If you have a policy against renting to rude people, that is perfectly legal. Plus you probably don't want a tenant in there that doesn't get along with the neighbor as you will likely be drawn into future squabbles.
Disclaimer: You should discuss your situation with a local attorney, as the above statement is a general overview and does not take into account all of the factual considerations in your case. Nothing in this statement creates an attorney-client relationship.