I think quality standards are a bit different from other trade barriers like tariffs and quotas. We in the EU are importing lots of foods from over the world and the quality standards are already in place and checked (or not, in any case we have to police this ourselves), so probably not much will change for e.g. Argentinian beef in that regard.
> but then their prices will have to go up
But again their prices would have to account for this whether they are trading inside the trade bloc or exporting to the EU.
> Another more cynical take is that were simply offloading to poorer countries the greenhouse gas emissions of our agriculture.
But we are doing this already. And if the issue becomes too big to ignore, we already have a solution, the Carbon Border Adjustment Mechanism, so let's apply that to agriculture too.