That political choice is "don't do anything about it, and leave it without a hard border". And this is the choice that both the UK and Ireland want to take.
That would be (from the UK side) the effective open border with the EU choice.
> And this is the choice that both the UK and Ireland want to take.
No, Brexit with the Irish border as an end-run around Britain’s new EU border is not a choice that has majority Parliamentary support in the UK.
For example, the US has, for years, refused to pass any kind of immigration reform, but until recently, also refused to comprehensively enforce the immigration laws already on the books because they were really awful and unfair in places. For another example, neither the People's Republic of China nor the Republic of China (effectively Taiwan) recognize each other, and yet Taiwanese businesses own tons of factories in mainland, PRC-controlled China.
It's pretty relevant, because the UK government doesn't have Parliamentary support for either of the alternatives, given Brexit, to the the thing they say they won't do, and also seems (though surprises are possible) to be likely to prevent Brexit from being derailed even if they can't pass a Brexit deal. So it's quite likely that we’re heading to a Brexit with none of the choices regarding the Irish border being politically viable.