The iMessage and text messaging system on the iPhone cannot be blocked by third-party developers (like Onward). Unfortunately, this means you cannot schedule Smart Filter to automatically block texts alongside your app and website blocking.
However, there is a method available to you to accomplish this (outside of Onward) called Do Not Disturb. If you change the settings on the "while driving" mode, you can easily block and unblock texts.
If you're interested in setting this up, please follow the steps below.
1. From the home screen, tap SETTINGS and then tap DO NOT DISTURB
2. Under Do Not Disturb While Driving, tap on ACTIVATE and then select your desired option. Choose the option that best fits your scenario when using your vehicle. If you don't use a vehicle, tap "Manually".
3. Tap on Auto-Reply To and select All Contacts
4. Tap on Auto-Reply and edit the message that will automatically be sent to your contacts if your texts are DND. We recommend something like "I'm offline right now. I'll read and reply just as soon as I can." Of course, you can customize this to say whatever you like.
5. Next, we'll configure Control Center to give you an easy on-off option for enabling this feature. To do this, tap on <SETTINGS at the upper left to return to the settings menu.
6. Scroll down and tap on CONTROL CENTER
7. Tap on CUSTOMIZE CONTROLS
8. Locate Do Not Disturb While Driving, and tap the green plus icon beside it to add it to your control center.
9. To access your text blocker, swipe up from the bottom of your screen to activate CONTROL CENTER
10. Now you should see a car icon. When you tap this icon, you will be enabling DND mode. Tap again to remove. While active, anyone who texts you will receive that auto reply and you will not be notified.
There you go! You've setup a simple system to prevent text messages and iMessages from getting through to you. Remember to turn this on and off when you don't want to be disturbed.