“1 in 10 residents” does not refer to a person but a proportion of people, which is a plurality of people. Change it to “10% of residents” and it’s clear that 'are"is more gooder.

If you want to super expand it…

A proportion of 1 in 10 residents are…

Or

Proportionally 1 in 10 residents are…

Aaand also…

“are” acts on “residents”, not “1 in 10”. “1 in 10” is an adjective phrase. Residents is the noun.