So, they want to add “not for EU” to products that are basically perfectly fine and legal to sell in the EU, because, why exactly? Some kind of weird reverse protectionism?
Because the UK chose to not be a part of the single market anymore, so goods they UK wish to export into the EU needs to be treated like any other 3rd country goods with checks and certifications to prove that they are good enough, but with NI still part of the single market as well as the UK, this label was the best solution they could come up with to avoid having to check everything going from the UK to NI. Without the label trade friction will be lower between Ireland and NI, which will please republicans, but not unionists I think.
To avoid tensions and economic issues, the Ireland/Northern Ireland border doesn’t have border controls or import duties. However, that means you have to prevent goods that cannot be imported into EU unrestricted from leaving Northern Ireland somehow (otherwise, people will start businesses that systematically circumvent duties). The solution the UK government has chosen here are “not for EU” labels.
Government plans to force food manufacturers to put “not for EU” labels on all meat and dairy products sold across Britain next month have been indefinitely postponed after warnings that the scheme could cause “chaos” for producers and suppliers.