Even the State admits that the chevra kadisha organizations, in large part, are out of control and listen to nobody but themselves, despite the fact that they are funded by the State.

I have heard many times that the chevra kadisha are like a mafia, making a lot of money, they keep the jobs for themselves, their relatives and friends, and they control what goes on at funerals with an iron fist. Obviously there are exceptions, and while I am not too familiar with the variety of organizations around the country, I can think of one or two of the ones I have encountered that are reasonable and flexible with special requests (to a certain point).

To that end, there has been a lot of controversy regarding the allowing of women to say a hesped, to eulogize, at a funeral, along with issues of gender-segregation. In general, the Religious Council has decided that women should be allowed to eulogize, should they want to, and the chevra kadisha should not deal with forcing men and women apart. It started with an incident in Kiryat Gat when the chevra kadisha did not allow the daughter to eulogize her father, and enforcing gender-segregation at the funeral.

Since then the issue has been raised in the Knesset and in its committee meetings a number of times. This week it was raised again in the Knesset when MK Aliza Lavi (Yesh Atid) raised the issue with Religious Affairs Minister Yaakov Margi, asking for a response to the complaints. Margi responded that his office has informed the chevra kadisha very definitively that signs informing of segregation should only be used as a recommendation, but segregation should not be enforced against the wishes of the family. However, Margi said, many chevra kadishas, along with many city and community rabbis, make their own rules and don't listen to anybody else, and basically he has not been able to control them. He says he is not giving an excuse, is not dismissing the issue, but explaining why the situation is what it is.. and he called on MK Lavi to use her influence and position, along with  his and everyone else's, to ensure that people do not get hurt and that there is no reason to keep women out of funeral ceremonies.
(source: INN)

With Minister Margi, from Shas, agreeing that there is no reason to ban women from participating in the ceremony  and agreeing that in a funeral there is no need for segregation (unlike in a shul during davening), the situation with the chevra kadishas should not be tolerated.

Margi says they make their own rules, they don't answer to anybody. That is unacceptable. they are operating through the State, via the Ministry of Religious Affairs, they are funded by the State, they should follow the rules or be made to. If a request goes against halacha, they can oppose it, and there should be a process by which such a request is passed along through proper channels quickly and efficiently so the right people deal with such situations. But when a request is not against halacha, and is simply something the chevra kadisha does not like or prefer, for whatever reason, they should not have the power or authority to reject it. Perhaps the entire chevra kadisha system needs to be dismantled and reconstructed. If they are unionized it might be difficult, but clearly some reform is needed in the structure of the chevra kadisha organizations.