How do I turn off the red underline in the Notes app?

Go to Settings > General > Keyboard > Check Spelling, and turn it off. This is a global setting that affects all apps. There is no way to only shut it off for the Notes app. If you do not want to see the red underline, you will need to shut it off. Auto Correction and Predictive Text options are not affected.

iPer007 wrote:

There is no Keyboard under Settings > General >

The Keyboard is not a subcategory, its on the same level as General.

Regardless, there is no Check Spelling under Keyboard

You always need to tell people what kind of device you are using. On a Mac, it is system settings / keyboard / text input / edit / for the spelling settings. Also on a Mac, every app has Edit > Spelling and Grammar > Check Spelling

iPer007 wrote:

There is no Keyboard under Settings > General >

The Keyboard is not a subcategory, its on the same level as General.

Regardless, there is no Check Spelling under Keyboard

What iOS version are you using?

The OP provided a screenshot of an iPhone, are you maybe looking on the Mac?

A screenshot would be very helpful in explaining what your issue is.

There is no Keyboard under Settings > General >

The Keyboard is not a subcategory, its on the same level as General.

Regardless, there is no Check Spelling under Keyboard