I always get so confused when 'they' is used for a single person. Is there any alternative? Everything seems to sound silly
It's perfectly standard. You're probably already accustomed to using it for a person whose identity you don't know, unless you walk around saying things like "I hope this person comes back to get his or her umbrella."
"Well officer, I saw them walk from their car up to the door then they turned and looked around, that's when I saw them pull the ski mask down, draw their gun and enter the bank"
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Manager: What was the customer doing when you told them to leave?
Clerk: Well I had been trying to help them with their project but they kept stepping into my personal space, then he places his hand on me and that's when I decided they'd crossed a line and needed to leave
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Most people wouldn't even bat an eye swapping they out for he/she in conversation in person.