Nobody is accusing any poster on mumsnet of being Hasbara, so I have no idea where you got that idea from?
The fact is that all countries have military units and civilians dedicated to posting on social media to disseminate favourable government narratives (The UK has the 77th brigade who are prolific online).
The Israeli unit 8200 has been extremely active online across social media, saying that is not an accusation.
Back on topic, 8 IDF soldiers have been killed and several casualties have occurred today as they tried to enter Lebanon.
https://www.bbc.co.uk/news/live/cg4qx62kkxxt