I'm at my wit's end. I'm using MMA version 220.127.116.11 (for Mac), and the front end is behaving bizarrely.
When I've chosen Subsection style, there are times when I'm writing that the front end randomly (?) upgrades the style to Section
Typing "=" in the middle of a mathematical expression sometimes (actually often) leads to the whole expression being converted to Text Display with a leading orange box with an equals sign in it
Other similar issues, for example a cell autoformatted to Python input
I've tried turning off things such as "AutoConvertEnable" in the OptionsInspector (is this even the correct option to turn off?), but clicking the box only makes the option bold, and the change doesn't stick. When I use a command such as "SetOptions[$FrontEndSession, "FormatTypeAutoConvert" -> False]", I can literally watch the OptionsInspector change from True to False with the use of the command, but then change right back to True again once I start a new line.
Edit: The version I was running was dated June 9, 2020. But the problems persist in the latest version I downloaded as of this morning, July 15, 2020, whose version is dated June 19, 2020.
When I change versions, I only replace the app in Applications folder. Maybe some files are stored elsewhere that got corrupted? Note that the problem persists even after wiping the /Applications/Mathematica.app/, /Library/Mathematica/, ~/Library/Mathematica/, and ~/Library/Wolfram/ folders (there was no ~/Library/Caches/Wolfram/ folder) and reinstalling.
Edit 2: Thank you very much to the two commenters who noted that starting any cell with "=" changes the cell style. I've been using the cleanly installed newest MMA binary (June 19, 2020) without a hitch. I believe the problem is solved, and so I'll accept the reinstall suggestion as correct. What a massive relief. Thank you all so much!