For starters, rather than give Ukraine a few billion dollars (hundreds of millions at the least), start with ensuring everyone has ID. Just start somewhere instead of offering excuses.
I don't think any would have an issue with that except Ukraine.
When you get pulled over by a cop, one simply can't say "i lost my ID" and the cop say, ok have a great day! They will give you a ticket to appear and prove all of that at a later day. Once proven, you're on your way. That's just one example where ID is a must and there's not an excuse that cop will allow you to use without a penalty for not having it while operating a vehicle.
The argument you suggested is that minorities often lose their ID or simply "do not have one". Do they get to use that excuse when buying a beer? Businesses can lose their license for not carding people. Employees get fired and charged. Business get hammered with fines. I know of a person who's life was all but ruined because they sold to an undercover cop without carding.
Voting in a country's election seems just a tad more important than that.
"I lost my ID, can I still vote?"
"Sorry, you cannot. However, if you genuinely wanted to you would go through the proper channels to get it, find it our wait until next time."
ID for voting seems like the one thing I'd bet 75% of Americans agree with. But if that's the case, 25% don't. You can't please everyone, but you start with leading the majority.