I live in a workplace where I have to identify my clients with their right pronouns like he/she/they. Since they're are only 2 genders and it is considered haram to be anything else besides these 2 genders. Would it be better if I quit my job and find another or can I make taqqiya?

If using the third pronoun is considered supporting something haram (like homosexuality) then it would be haram and yes you’d have to search for another job. But if in your society it’s not considered as supporting a sinful lifestyle like homosexuality, then using the “they” pronoun would be ok.

You can also be creative and just avoid using pronouns altogether. Instead of saying “he” came or “she came” or “they” came you can say “this person came.”