The US State Department does not really get to have a stated position other than diplomatic.
Will I as a developer or US business owner need to proactively disallow all users from outside the US (since I am not familiar with their laws) to avoid potential legal troubles, or will other countries block my site/service without me needing to do anything?
If you are, they can drag you to court. End of story.
If you aren't then they will first rely on your cooperation and if that doesn't work, probably issue arrest orders which will make it a bit inconvenient to enter the EU for a while. And they'll probably tell ISPs to block you, yeah.
That analogy is what I take issue with. It's clear that Facebook, selling ads to European buyers, is doing business there. But is every random web site with a few European users? Does putting up a web site suddenly mean you're doing business in every country in the world, subject to the jurisdiction of all of them simultaneously?
"The US State Department does not really get to have a stated position other than diplomatic."
Diplomacy is what it does, and its diplomatic position on trade issues is relevant.