On Mastodon, if you have posted in a thread or been tagged in it, you can mute the conversation so that you won’t see any more notifications from it. No one will know you’ve done this, and it will only mute notifications from that thread.
Log in through the website or a third party app such as Toot!, go to one of your posts in the thread, click ⋯ and select Mute conversation. If you haven’t posted, go to a post in the thread where you were tagged, then select ⋯ and Mute conversation.
If you change your mind, go back to the thread and select Unmute conversation.