If You Block Someone on Instagram, Can You Like Their Pictures?by David Wayne
When you block users on Instagram, they can no longer see your photos, videos or user profile in site searches. While they can't like your pictures, you're free to like theirs unless they also block you.
Avoiding People on Instagram
While Instagram doesn't notify a user when you block him, he may figure it out if he shares your followers, since your likes and comments are still visible to him. As long as you don't specifically mention his name in a comment, he isn't notified and may never see the comment. Since Instagram likes are anonymous, he has no way to know that you liked his picture. However, comments that specifically mention his name and include the “@” symbol are included in his push notifications, and he can see your username and reply to the comment. He can also send comments to you by mentioning your name and including the “@” symbol. For example, if your username is betty1990, you receive a push notification if he includes “@betty1990” in a comment.