Why does the Dawnguard attack me on sight?

I joined volhikar and become a vampire.

Yes. I am their enemy.

But what actually triggers them to hate me?

Is this because I am a 4th stage vampire? Does that mean if I drink blood I can come to Dawnguard fort and buy spells?

Is this because they know that the dragon born is an evil vampire that will kill them. Then why don't they tell everyone.

I am at destroy Dawnguard quest.

All guides say that I should cast harmony if I want to buy spells from them. Why?

Update: 4th stage vampire is NOT the problem. I feed on people. I talked with normal people normally. Yet dawnguard girls still hate me.

The most likely answer is that dawnguard can know my faction. However, this is very unusual. I joined stormcloack faction. I can go to imperial camps and they do NOT attack me on sight.

What actually triggers them to hate me?

The game's factions system controls whether another faction or group of NPCs hates (or likes) the player character. The player character is always a member of the "PlayerFaction" faction. I believe certain quest parts will have scripts that trigger this change in combat reaction, by setting how other factions react to the "PlayerFaction" faction.

Since you are already doing the Volkihar Clan's "Destroying the Dawnguard" quest, then members of the Dawnguard faction (and other related factions) have already been set to be aggressive to you.

From the UESP Wiki's "Factions" article:

Almost all NPCs and creatures in Skyrim belong to one or more factions (or guilds). These faction memberships control the combat reaction of all NPCs and creatures, both towards you and towards one another. You can be a member of more than one faction at a time.