Mastodon and/or Mastodon-compatibles really do need a "suppress this thread from my timeline" feature, like the "mute thread notifications" but for when you don't want to see it at all.
The fediverse server I develop, #snac ¹, has this feature with a Hide button. You can suppress full conversations or just a subtree of one. Further replies to hidden threads are also immediately dropped.

¹ https://comam.es/what-is-snac