Is there a way to disable the pesky problem Mozilla has with copying text from a web page
Mozilla always copies text from a web page _and_ HTML from the web page; it puts both in the clipboard, one in the "text" flavor and one in the "html" flavor (actually, sometimes it puts some image flavors there too, and so forth)
The app that you paste into decides what flavor it wants and gets it from the clipboard. If it wants HTML, it asks for HTML and gets HTML. If it wants plaintext, it asks for that and gets it. If it wants image data, it asks for it and gets it.
Sounds like you need to configure the app you are pasting into to ask for what you really want.
-Boris