Selling products and services would make them a hybrid (for-profit/non-profit) organization. The sales would be subject to sales tax. Without a 501(c)(3) status, they also wouldn't be eligible for many grants to secure larger fundings.
That's incorrect. You can sell products and charge sales tax as a non-profit.
Just look at the American Red Cross, they sell the blood that is donated to them.
You of course can't have a profit that is distributed at the end of the year. But you can keep "profits" in the organization for furthering the goals of the 501c3.