Yes, a person's beliefs are important and if their beliefs keep them from doing something, that should be OK with everybody. There are many people that have jobs that include responsibilities that go against what they believe and they choose to not participate in activities that violate their beliefs. If he is asked to do something against his beliefs and he resigns, that shows how strong his character is.
Waterboarding is a cruel practice. The CIA and other agencies have used this method before to force terrorist suspects and spies to talk. Since 9/11, the US has been on watchful guard, and has vowed to use whatever tactic is necessary to defend its homeland. Given that the US has strong allies, and has carried out several successful air bombing missions in the middle east, it may be time to step back and re-assess the role the CIA should take in dealing with suspected militants. In addition, the US is now preoccupied with several fatal shootings involving police and its own citizens to make waterboarding a top priority. If Brennan doesn't want to do it, there are reasons. He should not have to resign.
As a CIA director, you have the experience and knowledge to create and execute intelligence gathering. If you believe, waterboarding is not only against international law but an ineffective intelligence technique but are forced to do it anyway because, lets face it, politics. He has every right to resign because his hands are tied for him to do an effective job.
It would be different if John Brennan were refusing to waterboard suspected militants, but retaining his position as CIA director. However, he's saying that he will resign, which is completely respectable. He's not refusing to perform a job responsibility; he's refusing to perform his job if waterboarding is one of his responsibilities. There's a difference there. I think he's doing it the right way.