We are using PureScript in production at JusPay for both complete back-end and front-end.
Our complete code base(back-end and front-end) is in PureScript with as little JS as possible.
We use our purescript-presto library for writing business/application logic.
We use our purescript-presto-dom library, to write platform independent front-end UI which gets rendered on all the platforms(Android, iOS, PWA). Yeah, single codebase gets rendered on all platforms. 
Apps in Production
BHIM - Payments App, 17 Million Total Users
JuspaySafe - Payments Browser, 800 Million Txns Processed
JuspayFuel - Payments Solution for Gas Stations, 1000s of Outlets
Our SDKs are powering payments for Uber, Amazon, Foodpanda and many more.
(It’s safe to say that, almost each and every person in India using a smartphone is using some sort of PureScript application)