I can't comment with any degree of insight on the Tatler thing, having never seen the site. Yes, there is some vicious behaviour and persistent trolling on Mumsnet, and no small part of that comes from the 'manosphere', but there are some disgraceful comments posted to victims of male violence by women as well.
From the comments above there seems to be one major difference to me. One is a site whose sole purpose seems to be to troll and harass named individuals. If monetising children or child internet safety is the problem here then that's reprehensible and possibly even merits a report to social services. But there comes a point when relentless haranguing of particular individuals - who are also 'real' people - becomes as bad or sometimes worse than the behaviour which prompted this in the first place.
Conversely, this site is a parenting support site which is sometimes being misused. Importantly, it's also a grass roots pressure group which has resulted in political impetus to change some laws. It's enabled protest against exploitation of women (for eg., the aggressive marketing group targeting maternity wards). On occasion the site has highlighted valid world issues and brought about real impact and change. It's a huge site and of course not everyone appreciates these things, including those who hate women talking to one another about real issues that affect us. Arguably, it does need better moderation policies given how large it's become. It isn't faultless. But it isn't a site set up with the whole intention of harassing others.
You didn't personally mention the child abuse images targeted at this site, but I've seen reference to this above. Thankfully I didn't view the actual images, but I was around the next day and saw some of the fallout. This was a vicious and illegal trolling attack. Site members were universally horrified. All images posted to the site were blocked and moderated before cleared to post. Changes were made to the filters on the site, and the whole thing immediately became a police matter. The site founder posted regular updates to inform members what was happening. It should never have happened in the first place, but it was handled as responsibly as it could have been in the circumstances and as far as I know there has been no repetition.
As for 'Dr' Taylor: this is a woman with a PhD who qppears to have taken one basic premise - that PTSD/cPTSD are not necessarily best treated with medication like anti-depressants - but missed the important part of variation depending on the individual case. SSRI medication isn't the best for some people - I can't personally take it because of the soporific effect it has on me - but it's extremely valuable for others. Taylor appears to have taken these basic points and applied them as a blanket 'scientific' policy to all patients: what actual medical doctor doesn't know that individual bodies are different?
A maverick is very often a liability, cf. the 'Rt Hon' David Davis constantly interfering with what remains well beyond his political remit. People like this usually are usually liabilities, but when it comes to medical issues and seriously traumatised patients, they are actively dangerous.
Taylor can be a dubious practitioner, and Tatler can also be a radioactive forum deliberately set up with the sole end of haranguing named individuals to an alarming degree. The two things can be true at once.