One Reason on why Women are not permitted into Hatzolah is because although a female patient might feel uncomfortable when the emergency medical provider is a male.
however having a woman on the rescue team brings a lot of problems for the male members on the team. which includes problems like yichud. or problems of mingling.
this is something which the New Square Hatzolah must deal with and are having ‘problems’ with.
The rabonim and the coordinators know about this. and therefore will not permit Hatzolah to become a mixed organization.