Permanently disable "Check Spelling While Typing"
Solution 1:
Open Notes and go to an existing note or create a new one. Right-click in the body of the note. A menu opens and one selection is 'Spelling and Grammar'. Clicking on this selection gives you a sub-menu with selections for spell checking. Select the one you want.
Solution 2:
I just tried that on High Sierra.
The Check Spelling was Check-marked.
So I clicked on it to uncheck it.
Restarted Notes and it remained unchecked.