I wouldn't worry. It's popular in all of eastern europe and wikipedia even mentions the ukrainian origin of the most popular variant:

In English, the word "borscht" is most often associated with the soup's variant of Ukrainian origin, made with red beetroots as one of the main ingredients, which give the dish its distinctive red color.

Don't let a single whacko dictator ruin an otherwise nice dish.

I think not eating a food because of the country of origin is pretty dumb.

The Russian government didn't design borscht to be a symbol of Russian pride. Some grandma probably made it to feed her family. Also, borscht is the national dish of Ukraine. If they doh't have a problem with it then nobody should.

& there was me thibking it was also a Polish dish. Probably other countries too.