This has resulted in a call for this country to boycott the Olympics, if they cannot be moved to another country (which is very unlikely at this late date). I think this is a very bad idea, and it looks like most Americans agree. A new Economist/YouGov Poll (done between August 17th and 19th of 1,000 nationwide adults -- with a margin of error of 5 points) shows that a substantial majority of Americans (58%) do not think the U.S. should boycott the Olympics. Only 17% think a boycott would be appropriate.
This does not mean Americans agree with the new Russian law discriminating against homosexuals -- far from it. That same poll showed that 62% think society should accept homosexuality as a lifestyle, while only 38% believe it should be discouraged. And 63% think the Russian law is a bad policy.
The bottom chart gives us a clue as to why Americans oppose a boycott. A plurality of the public (45%) thinks boycotting an Olympics for political reasons is just bad policy. I suspect many others simply don't want to punish American athletes for the ridiculous actions of another country. These athletes have been preparing for this moment in the sun for many years, and for many, this will be their only opportunity to participate in an Olympics.
I do believe the U.S. government should do everything it can diplomatically to convince the Russian government that this is a bad law, and should be changed. And the International Olympic Committee should work to get assurances from the Russian government that no athlete from any country will be punished in any way for his/her sexual preferences. The Olympic games should be free of politics or interference from any government -- even the government of the country hosting those games. And all athletes should be free to compete without having to worry about hiding who they really are.
But a boycott is a bad idea. It will punish our own athletes, without changing the Russian law.