Sorry about the delay, I needed to stop for sleep and then go to work. The following is presented with the caveat that website hosting isn't my field of expertise within IT.
Big websites like Mumsnet are often hosted on clusters of load-balanced servers. These servers may be spread across the world for performance and resilience. A webpage isn't usually made up of content from just one server cluster, there will be pictures and scripts pulled in from many server clusters operated by different organisations. We can examine the page to find out where these scripts and pictures come from. It is commonplace for adverts to be pulled in from an advertising server cluster, as PPs have touched on, and it is the advertising servers' operator that Hailey wishes to target.
I can use the Inspector tab of Firefox's Developer pane to examine the adverts on the page and see what they are made up of. The adverts consist of content loaded into three iframes. (An iframe is a mini-webpage embedded within a larger main page.) These iframes provide the adverts that keep changing: one at the top and two on the right of the page. The iframes contain a lot of scripts that are responsible for rotating the content and have been written for speed rather than legibility. Fortunately, Firefox enables me to see the effects of these scripts by using the NoScript extension.
I open up a thread's page within Firefox and tell NoScript to "temporarily allow all on this page", even scripts from domains that I would normally consider untrusted. I also enable cross site scripting
and check that adverts are showing on the page. I then tell NoScript that I distrust each domain in turn, one at a time.
Distrusting googlesyndication.com stopped the iframe content from appearing at all and stopped the ads from being displayed. So I infer from this that Mumsnet are using Google Adsense for advertising. I can't foresee Hailey sitting down with Google over a cup of tea.
Google Adsense has policy on what content is acceptable on the websites that they serve content to:
"Incites hatred against, promotes discrimination of, or disparages an individual or group on the basis of their race or ethnic origin, religion, disability, age, nationality, veteran status, sexual orientation, gender, gender identity, or other characteristic that is associated with systemic discrimination or marginalization."
But the examples they give are very specific:
"Content promoting, glorifying, or condoning violence against others on the basis of their race or ethnic origin, religion, disability, age, nationality, veteran status, sexual orientation, gender, gender identity, or other characteristic that is associated with systemic discrimination or marginalization"
We've condemned such violence on at least one thread and haven't advocated violence against anyone.
"Content that encourages others to believe that a person or group is inhuman, inferior, or worthy of being hated on the basis of their race or ethnic origin, religion, disability, age, nationality, veteran status, sexual orientation, gender, gender identity, or other characteristic that is associated with systemic discrimination or marginalization"
We haven't done that either. What we have done is said that trans rights shouldn't come at the expense of safeguarding or women's rights and have provided evidence to support our concerns.
BTW Google, the protected characteristic you are looking for is "sex", not "gender".
The thing that sticks out on that tweet is "where the public can't intervene". That is a startling admission that Hailey knows that the public don't support the silencing of women.