The bigger problem is that Twitter and Instagram etc provide a platform for people to put on to the world wide web whatever they like with impunity and stuff like this, and much much worse stuff, is getting fired out onto the internet every second of every day, and it only gets noticed if you're famous enough for someone to trawl back through your posting history.
Really you should have to put some sort of legal identification when you open a social media account that only gets seen even by the website administrators themselves if something you post gets reported or triggers some sort of alert. There has to be some way to hold people accountable for what they post online if it's illegal or out of order because it's not acceptable to have a society where people can anonymously make racist comments or even preach hateful religious extremism whilst hiding behind a screen.
As for this particular incident though, another non story. People do and say stupid stuff when they're young and the misfortune of Twitter and the internet is that it makes it permanent. It's absolutely crazy though that any Premier League club doesn't have someone monitoring all past social media activity on official accounts of their players the second they turn professional. Choudhury could easily have had this flagged up by a club official a long time ago and gone and removed it before too many people saw it.