I understand that it's foolish to enable plugins on the Tor browser, because it could compromise my anonymity. However, I'm pondering whether it would be wise to just use another browser (like IE or Chrome) for the normal purposes (and enable plugins for this "regular" browser), and only use the plugin-disabled Tor browser for special purposes in which I'm concerned about my anonymity?
As long as you are using the Tor Browser with no extra addons and while using NoScript, websites cannot make an association between the two. Be sure not to use the same usernames, writing style, and so on over the clearnet as you do while using the Tor Browser, clearnet or not. It's definitely possible to associate your Tor browsing with your clearnet browsing if you don't take those steps as well.
Yes, that would be fine. If you are using a "regular" browser with no tor layer, plugins don't compromise the tor connection it is not using 😉
You may of course still not want to install a plugin that tracked you, but that is orthogonal to having tor installed or not.