When I booted up Krita today and opened a new file, I was greeted with a purple cursor.

When I started drawing though, I realised that the cursor was changing to the opposite of the colour beneath it.

I checked my Krita configuration and it was still set to the default green (#80ff80). Then when I went to use the line tool, it was lagging, showing a broken up circle as the second point.

I have tried resetting Krita, as well as reinstalling it, but neither of those worked.
Is there any way I can fix this?

Which version of krita are you using and which operating system are you using?
How did you obtain and 'install' krita?

What you show in the screenshot seems to be the 'Outline' and not the 'Cursor'.
My experience is that the outline is always a contrasting colour with whatever the local colour is. Having said that, I may not have been adventurous in trying different settings. I do notice that changing the cursor colour has no effect on anything, as far as I can tell.
I think you need a developer to explain that.

As for your noticing a change in behaviour, have you made any changes to anything recently?

Re-installing krita will have no effect at all. As well as resetting it by renaming (or deleting) kritarc, did you try also renaming (or deleting) kritadisplayrc?

I've just deleted the kritadisplayrc file and it worked! Thank you so much @ahabgreybeard!