Insert equations option greyed out

In order to use MathType with Pages v8.1, you would have checked the Pages Preferences : General : Equations: [√] Insert equations with MathType option. You need to deselect this setting before you can resume using the built-in Pages equation editor. You cannot use both concurrently.

Ensure that Pages is formally quit from its application menu. There is likely a Pages package folder (com.apple.iWork.Pages) in your local Library Caches folder that may be confused and causing suppression of the Equations menu item. Only a hunch.

Click on the Desktop to get Finder's attention, then press shift+command+G to open the Go To Folder panel, and copy/paste the following into it:

~/Library/Caches

Locate com.apple.iWork.Pages package folder with its conspicuous Pages icon, and drag to the Trash. Close the current Finder window.

Press the shift key while launching Pages. Choose a blank template, and see if the Equations is now available to you.

It certainly is possible that Pages could look within the system for evidence of MathType's installation and control the availability of the Equations menu item from that knowledge, but as a fellow user, and certainly without the Pages v8.1 source code, that will remain speculation.

Even if you uninstalled MathType, there would likely be residual files that it installed that would remain.

What a tangled web of MathType confusion. At least it is working now. Are you up on the blahtex converter that Pages is using in its own equation solution? It also supports direct entered MathML.