Learn German: Ich hoffe, dass du nicht allergisch bist.

When you want to negate a specific adjective, nicht goes directly in front of it. In a subordinate clause like this one (starting with dass), the conjugated verb (bist) is pushed to the very end of the sentence, so nicht and the adjective sit comfortably together just before the verb.

If nicht was negating the entire clause instead of just the adjective, would it move?

Actually, no! In a subordinate clause, when nicht negates the entire action, the rule is to put it right before the conjugated verb at the end. Because it also goes before the adjective it negates, the rules overlap perfectly here, and nicht stays in the exact same spot.

Can I drop the word dass like we often drop "that" in English ("I hope you're not allergic")?

Yes, you can drop dass, but it changes the word order! If you drop it, the second part stops being a subordinate clause and goes back to normal word order, with the verb in the second position: Ich hoffe, du bist nicht allergisch. Notice that you still must keep the comma; German strictly separates clauses with commas.

Why does dass have a double 's' in this sentence?