Turn off messenger

First, Facebook Messenger is a third-party App. As such, you may be best advised to seek assistance with this App directly from the App Developer - or support resources provided by Facebook.

That aside…

Sharing an AppleID is a very bad idea! Sharing an AppleID causes many practical and data security issues - not limited to unintended sharing of data and sensitive personal information such as Contacts, Calendars , Reminders, Notes, Messages, passwords and keychain data.

The Golden Rule: Don’t share an AppleID between users. Each user should have their own AppleID (and iOS devices) for their own exclusive use - linked to their own primary email (and secondary/recovery email addresses and trusted telephone numbers). 

If you are sharing an AppleID, you would be best advised to separate your digital identities - and if necessary create/configure a new AppleID for other users with whom you are currently sharing an AppleID:

How to create a new Apple ID – Apple Support

If your objective in sharing an AppleID account is to share App purchases, Apple services and subscriptions, you can do so properly using Apple’s Family Sharing features:

Family Sharing - Apple

Set up Family Sharing – Apple Support

Share App Store, iTunes Store and Apple Books purchases with Family Sharing – Apple Support

https://www.imore.com/how-set-up-family-sharing-iphone-ipad

Your problem/question is, at best, unclear.

You can use different Apps on different iPads without issues, opening and closing the Apps as necessary.

This user-tip may help you to explain what you are trying to achieve:

Writing an effective Apple Support Commun… - Apple Community