Android
Allow or Block Messages in Do Not Disturb auf Android
Do Not Disturb mutes sound and vibration for incoming notifications, but Android lets you carve out exceptions for messages. That exception is controlled by a separate People filter, not by the main Do Not Disturb toggle. If a contact keeps breaking through when you expect silence, or the opposite happens and urgent texts get muted, this filter is almost always the cause.
The setting lives under Tap on Settings ➔ Tap on Sound & vibration ➔ Tap on Do Not Disturb ➔ Tap on People ➔ Tap on Messages. From there you pick Select Starred contacts, Contacts, Priority conversations, Anyone or None.
Starred contacts only lets through people you have manually marked as favorites, which is the tightest option. Contacts opens it up to everyone saved in your address book, useful if you want family and coworkers to reach you but still block unknown numbers. Priority conversations follows the conversations you have pinned or marked important inside your messaging app. Anyone disables the filter entirely for messages, and None silences every text no matter who sends it.
Switching this filter does not touch calls or app notifications, those have their own separate rules under the same Do Not Disturb menu. If messages are still silent after allowing a contact, check that the conversation itself is not muted inside the messaging app.