I tend to agree with the protesters here, but I absolutely agree with you that there isn't much downside for Brin in taking this stand.
I actually think that tech titans like Zuckerberg and Brin may be in a role similar to Hollywood stars in politics, but maybe even worse. Truth is, the H1B visa isn't really a visa that "allows" foreign workers to come to the US, it's a visa that allows corporate HR departments, largely in high tech, to decide who is and isn't allowed to come to the US - and the conditions under which they are allowed to stay. It's a remarkable power, an unacceptable one in my opinion. Although I'd be opposed to this kind of corporate control over the immigration system in general, I think that google showed itself very specifically unworthy of this power through its involvement in the no-poach collusion. But again, this is what I've come to expect - in fact, I'd say it's very naive to believe that handing corporations control over a big wing of th immigration system wouldn't lead to corporate mischief and an erosion of basic human rights for the workers whose lives they control.
If google, Zuckerberg, and so forth lobbied fiercely for greater freedom for immigrants - freedom to choose what they study, what companies they work for (if any), freedom to move... really, just basic human freedom, then I might be more interested in this sort of stand. Otherwise, I tend to be deeply suspicious of their motives the moment they start to speak, because I know they have a political agenda that involves gaining control over the immigration system.
But as it stands, I think that a lot of Silicon Valley "elites" like to wear the halo of being pro-immigrant while lobbying for a program that allows them to determine the circumstances under which would-be immigrants are allowed to come to the US and stay here. Just like the no-poach agreement, they use this to create a workforce that isn't allowed to participate freely in free labor markets, which I consider to be an essential component of basic human freedom.
As you can tell, I don't care for them much anymore. And yeah, this was a personal transformation that took place over decades - there was a time I admired them.