I don't think you understand how these things work.
First Red Cross is a medical disaster charity, not a homeless program. They show up to scenes of disaster and provide medical assistance to those who need it on scene. For example, when my apartment building burned down, they arrived within minutes after the firetrucks. They provided water, blankets, and oxygen on scene to any who needed it.
As for Homeless shelters, I actually have volunteered at a few. Before you cast a judgement on a homeless shelter, I propose you do the same. First, the biggest problem with Homeless shelters is they are extremely underfunded and they help on a first come first serve basis, on a "who is in the greatest need" and generally they help families with children first. Yes, they will actually make a single person leave to make room for a family with children. Basically it works like this, they take people until they reach firecode capacity. Once they reach firecode capacity they have to turn people away. The law forces them to do this. They usually try to give them other resources and information where they might go, but if they are already aware that all shelters are beyond capacity( which is usually the case) they can provide a blanket, and possible a box if they have blankets and boxes available and tell them to try and keep safe. That isn't because they don't care, that is because they do not have any more space or resources available. I would not expect a homeless shelter to respond to an email, because the truth is, if you have somewhere that has a roof over it and internet access, you are in a much better position trying to stay there than you are trying to come to a shelter. If you have internet access from anywhere, you are better off than 99% of the people coming into the shelter. If you have phone access, you are better off than 99% of the people coming into the shelter. The shelter is a last resort, and do not expect to get help from one unless you go in person. Even sleeping in that persons back yard is BETTER than a shelter. Shelters are not fun places to go, they also have to try to screen you to try and reduce crime at the shelters and protect the people there. That is if you can even find a homeless shelter. The lack of funding is why we also have tent cities popping up everywhere. The few that are actually able to keep their doors open have so many people trying to get in them, there is no possible way to help them all. Most shelters have a waiting list, even for families because they already are full of families, and have to force out families who have had a roof over their head longer than those who have been waiting in the streets.
Before casting judgement on these organizations, you should try to volunteer for them and see first hand where your money is going.