The difference between the racist comments and the transphobic commenters though, is that the racist ones get challenged and they're not in the minority when they do so.
I have seen transphobic posts challenged, a lot. I have also seen, more recently, that those transphobic posts posted by brand new (and honestly, suspicious..give the second they post their bile its screenshotted and on twitter as proof of how vile we all are
) accounts tend to be just mass reported, and ignored. on the whole. Which honestly, I think is the best way when its quite obvious its a troll account. I would say the same if it was someone joining purely to spew racism..especially if there was a BAME section of the site (is there..I have no idea as theres literally loads of sections) and these racist twats mainly posted in there when they 'joined'..like the MRA/TRA types do. Its extremely rarely a longtime poster, and even more rarely a long time poster who frequents the feminism section. And when it is, its challenged, along with reported.
If a site quickly removes transphobic content, how on earth can it be claimed that the site is transphobic? Even if we were to take these brand new users posting actual transphobic posts as genuine new users, all that proves is that trnashobies join and post shite. If the site left such transphobia standing, then yes, it could easily be argued that the site is transphobic. But people use 'transphobic posts are deleted quickly' as a way to somehow prove the site is transphobic?! Bizarre and nonsensical really.
The misrepresentation of threads in feminism is quite silly too, people can read the threads themselves you know? I know the theory is, say it enough and some will believe it..but its a ridiculous way to 'prove' anything tbh. The 'people said a crime committed by a woman has to be a transwoman as a woman wouldnt do it' turning out to actually be 'papers seem to be reporting male crimes as female crimes yet again, yes a woman could do this in theory, but its largely a male type crime and given previous experience, the press are not above this nonsense' is just..weird. Especially when linking the thread to 'prove it' when the thread says the opposite of what was claimed.jusy..odd behaviour. But each to their own I guess 
In short, I would be interested in finding out quite how the fact that transphobia is quickly deleted, proves the site is transphobic. If anything, I would ay the opposite. Some anon users are transphobic, but they are removed almost immediately. Because mumsnet does not tolerate actual transphobia. Mind, if you are one of those who reckon even acknowledging that males and females are different things..or that stereotypes are masively important and should be followed else theres a problem, then yeah, I can see why you see transphobia everywhere on here. But really, a site that has a large focus on having/bringing up children and such, will generally acknowledge the role of biology in life, you know? Along with mums knowing kids are into everything, and stereotypes matter not one jot. Maybe, if you focus such importance on stereotypes and such, or wish to claim that changing sex is actually possible and anyone who disagrees is a nasty bigot, somewhere like this is quite likely to upset you..