There are a lot of reasons why women are excluded. In my experience in the north it's primarily racism and discrimination.
I had a first nations woman who went to the family violence shelter to get an emergency protection order. She wasn't even allowed through the door. They talked to her from the door and said that she couldn't get the emergency protection order because her abuse wasn't serious enough or sustained enough. The very next day her non-indigenous partner went to get an EPO at the same shelter, and he got the EPO. Then she was separated from her five children for the next five years. She's still trying to get that done.
Women with alcohol, even if they smell of alcohol, are not allowed in the shelter. Women who go out three times in a row and don't report back are booted out of the shelter. There are a ton of rules that prevent, especially indigenous women, from accessing or staying in the shelter.
One of the Inuk women lived in transition housing for eight years. She said when she moved out into subsidized housing it was like she got a pass out of jail, after eight years. She felt like she had been incarcerated.