Not able to see X posts. However based on your information, I think they are right. As the leader of a sex based refuge service and Chair of trustees of a rape crisis service for women only.
As a charity we have to avoid any kind of political alignments whatsoever, and any controversy.
Equally commercial branding can become problematic. We had support from a local car industry leader, whose women's marketing group, took an interest, and did some fine fundraising, but they came to believe they could dictate how we were run.
My agency many moons ago turned down something called the a “strong man’s”competitive events, which i see has grown.
There was nothing wrong with what they do per say, but the connotations for a domestic abuse agency was clear so we had to turn down the offer.
Charities do need to be mindful of who they accept money from.
on the other hand we got money for several years from a huge brand, and products such as towels bedding, toiletries and actionable collectibles. No public acknowledgement was wanted or required.
For charities to maintain independence and avoid mission creep they also need to fight shy of too much public funding. That is how women only services have got in to the pickle they are in.