I am assuming your father does not have an abusive streak, since you say you’ve both been close except for this one issue. However, if I’m wrong, and he has been violent in the past or hit you — please ignore my above advice. Unreasonable, violent persons would take all of the above as a challenge and might lash out.] I know you might wish you could force him to change his views, but that’s not possible until he’s willing to change them. And in many cases, bigotry, racism and homophobia are life-long, deep-seated issues within a person’s psyche — very difficult to change, even for the person who holds those views. Trying to force the issue generally results in them digging in their heels and becoming even worse about it. After all, you are challenging an intrinsic part of their world-view, and that’s not easy to hear or accept. They don’t believe they are wrong, and being told they are is a very hard pill to swallow.
If this person were a friend, I wouldn’t advise working so hard to preserve the relationship. Those sorts of attitudes are hard to shift and overall, not worth dealing with. But while it’s easy to dump a friend and find new ones, this is your parent. He will always be your father, whether you like him and his views or not, and you will always have to interact with him on some level. (Even if you outright rejected him and refused to see/be around him, he would still be part of your life — even if only as an issue in your mind you’d have to deal with.) You say he’s been a good father with this one exception and you don’t want to cut him out — so my advice above is the best solution I can see to maintain that relationship.