AlwaysOn Setup New User on Read Only Replica

All you need is to create the same login on the second server preserving it’s sid, and you can do this first by copying the login’s sid from sys.server_principals and then by creating the same login using with sid like this:

create login my_login with password = '*****', sid = 0x6E94CADC0A6EEC439B620643CDDB5C71 -- put here your login's sid 

Example:

On Primary Database:

USE master
GO

select * from  sys.server_principals

-- name = user01
-- sid = 0xA72A66203E6C3743B9500EE520BD1234

On Read Only Replica Database:

USE master
GO

create login user01 with password = 'test123', sid = 0xA72A66203E6C3743B9500EE520BD1234

Sources:

https://dba.stackexchange.com/questions/174946/creating-a-sql-login-and-user-on-an-alwayson-replica