Neither. Gmail is an email provider which has provided access to an account that these people have registered with providers of vital services.

And? Not every service is homeless-friendly. That's fine. There are literally hundreds of free email services.

Why is it fine? Why should we not ask and expect that one of the largest corporations on the planet make a tiny effort to improve the lives of some of its users at very little cost to them?

Sure, homeless people and those who help them should pick an alternate free email service. And the government should either set up its own email or stop requiring email contact for this sort of thing. But for people who are already Google users, Google should also try to make their lives significantly easier with a tiny bit of effort (allow someone to explicitly disable 2FA for gmail - with all the warnings and cautions that they can).