Views switches to another view on apply or any change
I finally tracked it down to a setting in Views (where it shows all of the views) and the Settings tab. Under the Advanced Option here, I was able to turn off a "Disable Javascript on Views" setting that had somehow gotten turned on. The Ajax function was not firing and the main URL was resetting for every update of any kind. This meant jumping between views for every change of any field whatsoever.

That setting fixed everything though, so I'm posting in case anyone else has the issue and can't find a reason.