Cannot turn on notifications for reminders

Greetings tstrawbridge,

Begin by making sure there are no restrictions or parental controls in place that may be preventing your from making changes on the device.

Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

"Allow changes to other settings and features

You can allow changes to other settings and features, the same way you can allow changes to privacy settings.

1. Go to Settings and tap Screen Time.
2. Tap Content & Privacy Restrictions. If asked, enter your passcode.
3. Under Allow Changes, select the features or settings that you want to allow changes to and choose Allow or Don't Allow. 

Here are some features and settings that you can allow changes for:

• Passcode Changes: Prevent changes to your passcode
• Account Changes: Prevent account changes in Accounts & Passwords
• Cellular Data Changes: Prevent changes to cellular data settings
• Reduce Loud Sounds: Prevent changes to volume settings for safe listening 
• Driving Focus: Prevent changes to the Driving Focus
• TV Provider: Prevent changes to TV provider settings
• Background App Activities: Prevent changes to whether or not apps run in the background"

Take care.

Hello tstrawbridge,

Welcome to Apple Support Communities!

We want to make sure the notifications are showing as expected.

Please also check for any pending iOS updates, which can help make sure the software is working as expected. This Apple Support page can help get those updates installed: Update your iPhone, iPad, or iPod touch - Apple Support

"Update your iPhone or iPad wirelessly

1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. Choose the software update that you want to install. You can choose to stay on iOS or iPadOS 15 and still get important security updates. Or you can choose the option to upgrade to iOS or iPadOS 16.

5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do."

If the issue continues, please reach out to an Apple Support Advisor for further assistance: Get Support

We hope this helps to resolve the issue so you can adjust the notifications for the Reminders app.

Cheers!

I'm having the exact same issue on iOS 16.0.3. It's not related to parental control and notifications on every other app work just fine.