I think it is saying that Mumsnet had previously been used by Koschate at Exeter, to successfully distinguish between "feminist" and parent "identity" (I have questions about that but never mind). It's not saying that Liu used Mumsnet at Lancaster.
"ASIA (Automated Social Identity Assessment toolkit) (Koschate et al., 2021), a toolkit which leverages machine learning and natural language processing to automatically assess which identity is situationally salient through sociolinguistic styles, has been proven to be successful in assessing feminist and parent identity in Reddit and Mumsnet online communities."
So, I have had a quick poke on Google Scholar for ASIA Koschate 2021 and found 2 papers
https://link.springer.com/article/10.3758/s13428-020-01511-3
https://ore.exeter.ac.uk/repository/handle/10871/124775
The first one says that MumsNet gave permission as followsL
Proof of concept: Ethics
For our proof-of-concept case, in which we aim to detect parent and feminist identity salience, we chose identities that are widely held and not highly stigmatized. We collected the datasets with permission of the platform owners (Mumsnet UK, Netmums UK) or where permission for research use is granted by the terms and conditions (Reddit). All three platforms explicitly inform users that any content created is in the public domain and rights are owned by the platform rather than the user. Furthermore, forums on all these platforms are clearly signposted as being in the public domain rather than a place for private conversations, and therefore do not fall under the principle of “reasonable expectation of privacy”. For instance, Netmums UK calls their forum “Coffeehouse” to indicate its public nature. All of these platforms allow private messaging between users, thereby highlighting the distinction between public and private channels. No private messages are included in any of our datasets. All five studies presented here received ethical approval from the University of Exeter psychology ethics committee.
Later on they say:
The online forum data for training our model were gathered from the online website Mumsnet UK (www.mumsnet.com/talk), the largest parent online network in the UK, with the kind permission of Mumsnet UK. This site provides different sub-forums in which users can discuss particular topics and themes. We analyzed posts from two sub-forums, “Being a Parent” and “Feminism”. The posts were collected in September 2012 from 2500 threads per sub-forum.
I wonder, did they get permission from Mumsnet to look so specifically at feminism and the Feminism board?