I am homeless and a homeless advocate. I agree with you. Email addresses can be had for free and accessed for free via, for example, going to a public library.
I am online all the fucking time, even when my tablet or laptop has died and I don't yet have the means to replace it. Sometimes I have a phone. Sometimes, I don't. I have yet to find a 100% free and reliable means to have a phone number.
80% of Americans below the federal poverty line have cellphones. (http://www.cnsnews.com/news/article/terence-p-jeffrey/census...)
1) More than 92% of Americans have cell phones[1].
2) An SMS/MMS-enabled number is free from Google Voice.
3) Cell plans don't require credit (except possibly for the phone itself). You can pre-pay.
4) This may be discrimination, but so is requiring an email address. The question is whether it's illegal discrimination, and the answer is no. "Phone type" is not a protected class, like race or religion, in the United States. "Income level" is also not a protected class.
1. http://www.pewinternet.org/2015/08/26/chapter-1-always-on-co...