If a user has DNT enabled, Matomo considers this as a sign that the user wants to opt-out of tracking and doesn’t save the data at all. All requests are immediately dropped once Matomo reads the DNT header.
You can even add _paq.push(["setDoNotTrack", true]); to the tracking code which causes Matomo to not send data at all if DNT is enabled.
Of course you can disable this setting and therefore make Matomo ignore the DNT header.
There has been a discussion about a limited tracking of DNT users here:
Personally I am not a huge fan, but can understand the use case.