"I cannot fully support your work while you continue to promote these ineffective, unsound, and at worst dangerous products."
Is there evidence that homoeopathy is dangerous for use in childbirth? I thought they were fundamentally sugar pills ? 
You might want to contact them about the fact they offer TENS machines for hire as well. Their literature suggests that some labouring women find it helpful. NICE guidance is that TENS use shouldn't be discouraged, but shouldn't be offered or suggested because there is no clear evidence that it works.
I personally think it's great that the CEO took time to respond to your letter at length and reconsider the stance of the charity of homoeopathy.
Out of interest, if it's made clear to purchasers that homoeopathy has never been shown to be more effective than a placebo in any decent quality clinical trial, would you still feel that it's unethical to sell it? If there is also no evidence of harm in its use? Would you also ban of TENS?
here This is a critical review of the evidence on complementary treatments in pregnancy and birth by the NCT from 2009. It doesn't have anything positive to report about homeopathy.
"- choosing to have a prospective father to write their 'expectant parent's diary' for months on their blog (instead of, not as well as, a prospective mother)"
NCT is a charity for expectant parents. About 90% of the material on the website is primarily focused on the needs and experience of mothers.
"- not having ANY classes for women only or for pregnant people only (i.e. all classes are couples and include men)"
There are women only classes as part of many of the antenatal courses. Not all.
"- appointing a man as their new Chief Executive"
It's a charity for expectant parents, and he's a dad!
But even if he wasn't a parent his job is to run the charity effectively. His gender or status as a parent shouldn't be an issue.