I think people might be getting euro pallets and heat treated pallets mixed up.
The way the term is usually used these days (I'm going on experience as a stock controller at a small wholesaler) a euro pallet is something different from what is being discussed here. What most people in the trade would call a euro is just a pallet that's 1200x800mm. You can send other sizes in the EU but its cheaper to send these with most of the couriers and road freight companies.
That bit doesn't change if we leave with no deal.
Anyone outside the EU has to send goods on heat treated pallets. As an EU member (and a country where none of the pests are actually native) we're exempt.
Its not as simple as them needing to be blue either. I'm pretty sure all the blue ones, as @Sprocket says, all belong to one company, they're sort of weirdly leased but I've never worked out how they get them back. I don't know if these pallets are heat treated. It could be they have some kind of stamp that the EU accepts but that seems pretty relaxed and unlike the EU. This is the only bit I'm not 100% on.
Obviously if we leave with no deal the EU will deal with us on WTO terms which means the same as everyone else so no exemption.
If its anything like sending to China and most of the far east, where there are similar requirements, you need to send a heat treated pallet with a certificate to prove it is heat treated. In effect it means they can't be reused and you need to have a pallet treated every time you send to the EU.
Or you can use plastic pallets. No certificate required.
Pickers may want to correct me on any of that.
