So, it started in a post in 2012 (or earlier, I don’t know the exact date). As the Urban Dictionary entry explains, you would say “I like your shoelaces” in public as a sort of secret code if you suspect there’s another Tumblr user there. And if there is another Tumblr user, they would reply “Thanks, I stole them from the president” to let you know they understood the message and are, in fact, a Tumblr user.
I don’t think people do this anymore, and if they ever did, it probably wasn’t a very common thing to do. Maybe they did back in 2012 when the post was recent and Tumblr wasn’t as popular as it is now.
I also don’t think there’s any deeper meaning to the phrases. “I like your shoelaces” seems like a pretty common and nice thing to say, and if it turns out the person you thought was a Tumblr user doesn’t recognise the ‘secret message’, nothing would happen. But then “Thanks, I stole them from the president” seems weird and specific enough that you would know they understood the ‘secret message’, unlike if they just replied “Thank you”.
Then other posts appeared making references to the shoelaces and president posts:
A Glitch Named Anti 