My assumption is that you reduce both your HP and max HP by half your level when activating Rite of the Dawn, and that the ability description forgot to specify that the max HP reduction is also halved. Meaning that you'd suffer 2 damage and reduce your max HP by 2.
Based on the text, the Max HP reduction remains the same. The Blood Hunter lists the amounts for both effects explicitly. You take damage equal to your level, and you reduce your Max equal to your level. It does not link the Max HP reduction to the amount of damage taken the way a vampire bite reduces your max HP based on the amount of necrotic damage you take. This does result in a situation where if you activate Rite Of The Dawn when you're at full health, you'd effectively be taking the full damage, since the Max reduction would take you below what the damage is. I have no idea if this is an intended quirk, or if Matt Mercer intended the Max HP reduction to be halved as well. If you're really curious, you can probably ping him on Twitter and ask, he's usually quite good about responding to such things.
They are technically separate effects, but I do believe the intent behind Rite of the Dawn is that the HP reduction is halved as well. I can see a reasonable argument either way.
That's why I suggested contacting Mercer. A straight reading of the text described the reduction of Max HP in a way that isn't dependent on the damage-taking effect, but since he didn't have the WotC editing/proofreading team, it may have been an oversight. If he meant them to be linked, he may want to update the official text. Hell, I may tweet at him myself to see what he says.
RAW you would take reduced damage, but your max health would be reduced by the full amount. This might be a relevant distinction for class features or magic items that reduce damage or prevent the reduction of max health, but is otherwise straightforward.
RAI... I don't see the point of reducing the amount of damage you take, if the amount of max health lost is not also reduced. It is self defeating if treated that way, and as such I see no reason why the reduction should not also be applied to the max health lost.