Judging from this very polemic article by linguistic anthropologist Kathryn E. Graber, the argument is that a linguistic distinction that exists in Russian (and Ukrainian) is mirrorred in other languages using the definite article. 'Na Ukraine' on the one hand literally means 'on Ukraine', 'v Ukraine' on the other 'in Ukraine'. Graber goes on to say that 'In Russian, a person is “na” an unbounded territory, such as a hill, but “v” a bounded territory that is defined politically or institutionally, such as a nation-state.' She would then probably also argue that the same, in English, goes for names like 'the Congo', being named after a river. The claim that this is a Soviet-era practice (if what she means by that is that it arose during the Soviet Union), is simply not true, though. In Google Books you can find plenty of titles with 'the Ukraine' from before 1900. The earliest mention I found in English (though I didn't look very well) was from 1672.

It anyway strikes me as very performative. You can well argue that language influences the way we view the world (though, I think the way we view the world influences the language we use much more). Even so, there are obviously much bigger (concrete) threats to Ukrainian sovereignty than (to Ukrainians) foreigners using a definite article or not. Thus, it becomes less a matter of protecting sovereignty, and more a matter of simple respect to Ukrainian sensibilities. Ukrainians may take offence at you using the definite article, and you may want to prevent that by not saying 'the Ukraine'.