I know it didn't make much sense, but I wanted to play as a "good" vampire and hunt down the evil vampires. However, even though I was a vampire when I joined the Dawnguard, and Isran didn't notice, they had him change his mind moments later. I get the test part. I failed his test and had to go get cured. But after I was cured and I talked to him, I became a vampire again and now he refuses to talk to me. If he needs his test to tell who is a vampire, how does he know that I became a vampire again without retesting me?

I just found him the moth priest. When I walk near him, he compliments me, but when I talk to him, he insults me and tells me that I'm dead to him. I don't like this.

Here is the problem your a vampire and you are in a group of vampire hunters. As you said it does not make much sense, you can't have your cake and eat it too.

Then why did the idiot let me join in the first place? There have been a number of vampires-who-hunt-vampires in other works of fiction. Using their own talents to fight them. Just moments ago, he agreed to let Serena help out, but heaven forbid I help out. The Dragonborn who saved the world.

You're allowed in initially so that you may have a taste of both factions before choosing one. As for the dialogue discrepancies, that's always been a lack of polish prior to Dawnguard.

No he does not like serana he does not consider her a person only a resource/asset and if she steps out of line even once its your ass on the line. Plus he wanted to butcher her right then and there but your PC plot powers saved her. As zexis said its also a lack of polish.

Personally, I would have liked to pull a Seridur. But alas, that's only initially possible.