I was in grad school during the peak Free Trade/globollocks area. There was a lot of focus on "non-tariff barriers," in part because trade was a hot topic and economists needed to publish papers on it, but in large part because it helped to serve the broader ideological agenda of neutering the state.
A lot of it was very silly. The EU was still coming together and a big debate was about "country of origin" labeling. This was the kind of thing that was touted as a "non-tariff barrier," as if it was somehow unfair to tell Germans that a package of lamb was from Britain and let them choose accordingly. The belief (of some) was that consumers shouldn't even be allowed to care about this stuff - where it was produced - if our glorious frictionless flat world was to be achieved. Unfair!
More broadly, you can basically call any involvement of the state a "non-tariff barrier." A slightly different regulatory system? A trade barrier! A country invests in infrastructure? A trade barrier! A slightly different system of taxation, such as a VAT tax? A trade barrier!
The only way around this is for the state to disappear entirely.
