Personally I did not use the Facebook app and do not have or want the messenger app. But I do need to have access to messages people send me.
The work around is simple, find a browser such as chrome that has a built in ability to request the desktop version of a website. (Or find the link at the bottom of the Facebook page, very hard to find)
Load up Facebook, click on the friends tab, now request to load the desktop version of the site. On chrome it's the 3dot options button, request desktop site. The site reloads, now click on the messages tab and you can view and send messages without the pop-up that sends you to the playstore.