If you're tired of getting new message alerts from a frequent texter, you turn them off without blocking them entirely. You'll still get an alert if someone important sends a message, but your phone will no longer buzz if you get a message from the chatty person.
It's really easy to do, but it's kind of a hidden feature. Here's how to do it.
That's it. You'll still see a little red dot if you've received a message, but the conversation won't flood your phone with pings and notifications. It can be reversed, too, by following the steps and toggling "Hide alerts" back to off.
If you're stuck in a group of chatty people on an iPhone, you can also easily leave that group by tapping the same "i" button as before, and then choosing the option at the bottom of the page to leave the group.
This only works for iMessage groups, so it won't work if you're in a group conversation with people using Android phones.