If you don't want to see someone's posts in your feed, see their stories at the top of your feed or see incoming messages they send you, there are multiple ways you can mute someone on Instagram.
Instagram won't let them know you muted them. Keep in mind that muting someone is different from
unfollowing them.
Mute or unmute messages
To mute or unmute messages from someone:
Mute or unmute posts and stories through their profile
Mute or unmute an account through feed
Keep in mind that muting someone’s messages, posts or stories will not apply to notes they share. You will still see notes they share on Instagram. Learn how to also
mute someone’s notes.