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Remember how #twitter doesn't show your replies in your tweet feed?
In #mastodon , you can differentiate between "Public" and "Unlisted". You can reply with the setting "Unlisted" if you don't want your replies to clutter your profile. E.g. courtesies like "you're welcome", or if the reply is only relevant in context of the thread.
To do that on the web client, click on the globe icon below the compose box, and choose "Unlist".
You can also change the default to "Unlist" or "Followers-only". To reach that setting: scroll down the right side bar, Preferences > Other > Posting defaults > Posting privacy.
@kemuri Thank you!