As per the title, should tourists with a darker skin color (i.e. darker than is common in Eastern Europe) expect any issues or hostility nowadays? If so are there are ways to mitigate this, perhaps travelling in a group or avoiding certain areas?
When I stayed in Tbilisi a few years ago I met quite a few people from African countries and Americans of African descent.
In the circles I moved in they were all accepted 100% the same as the people of other skin colours in Georgia.
Now my circle was the kind of people that owned and ran backpacker hostels and student bars, so might not be representative. For comparison, gay people were also accepted in these circles whereas they are are not well accepted in Georgia generally.
Also I don't recall meeting any Africans, African Americans, etc in any other part of the country, so I can't say if people's attitudes vary from place to place or not.
Georgia is very culturally diverse though, being at the crossroads of Europe and Asia and has quite a lot of people with "in-between" skin colours such as Arabs not to mention the diversity of religions. Tbilisi is one of the very few cities in the world to have a Christian church, Jewish synagogue, and Muslim mosque on the same street.
Personally, I think you'll love it. A great place to start meeting the right kind of people when you get to Tbilisi is Canudos Ethnic Bar.
I am Georgian and simply we love tourists, anyone outside our country who wants to visit anything related to Georgia we appreciate it alot.
This country is very hiddend from the media and only shown wars back when there was Stalin and most people think its part of Russia.
Hospitality is a massive thing in Georgia, if you were black ,green or any colour and needed to stay somewhere we would invite you in, give you wine and food.