Firefox has a Bookmarks Toolbar you can turn on/off. This typically is below the address bar -- from top to bottom:

• Title Bar (optional)
• Menu Bar (optional)
• Tabs
• Main toolbar
• Bookmarks Toolbar (optional)

If you used to be able to put bookmarks directly on the menu bar, or anywhere other than the Bookmarks Toolbar, your bars probably were customized, and/or, an add-on was involved.

Could you help me get a better understanding of your current setup?

Are you saying the icons are changing position? I take it you have not changed anything?

Are you using sync?

If you have sync, and there is a problem anywhere, Shut Down Sync Immediately On All Devices to prevent the problem from spreading. Once the problem is fixed, perform the same repair on all computers/profiles before using sync again.