Russians of any gender or minority could vote for their representative in 1917. Women in the States only got full suffrage in 1920, African Americans in 1965. So no real pedigree there.
But a whole state-level legislative architecture meant that suffrage wasn't accessible nationwide till the Voting Rights Act of 1965.
Modern voter registration laws, which are gathering pace today, are largely targeted at keeping minority voters from exercising their democratic rights.
The US has generally had elections in which whether you could run did not depend on your ideology or opposition to the current administration, and the candidate who got the most votes would get into office. Russia, not so much.
