Hm, maybe if we start lobbying for open borders, immigration haters mobilize and start pushing for closed borders and it all ends up with visas for Russians being banned. Is that kind of thing likely?

To be honest,  I don't think this donation will do anything, and not just because the media is blocked. Putin supporters do not read liberal media like Meduza, so it is not going to change minds. What it can do is call thousands of liberals to peacefully protest on the streets. As we have been doing for the past 11+ years, with zero effect. Unless millions of people join the protests (which they won't, not until sanctions cause famine or something) or protests turn violent (which they won't, most liberals firmly believe in nonviolence), Putin is just going to ignore them, like he did all these years. These protests are not effective.
Ukraine's resistance, on the other hand, is having an effect. They only fought for one day and Putin asked for negotiations. They're destroying the myth of Putin the strong leader, who's going to unite slavic lands and bring back USSR. Sanctions are destroying the "stability", the second reason people supported Putin. Dead soldiers are a more convincing argument against war than all the words we can say and have said for the past 8 years. That's why I believe the effective thing to do is to support Ukrainian army, call for more sanctions against Russia and help the refugees.

In USA, Congress could pass a law like this. What if all American rationalists/EAs write to their Congressmen or meet them in person and ask to give asylum to all Russians and Ukrainians with a path to green card? (I see no reason why give asylum to Russians but not Ukrainians, and the idea might be more popular this way). I don't know much about American politics, is there any reason not to try this?