So what makes Asda different from the rest
I see two reasons. The official one was that going to supermarkets for anything than food at the beginning of the lockdown was frowned upon and discouraged. The second reason is that HUKD gets no commission/kickback form in-store deals but they still have to check and moderate those posts what costs them money.
They make some very strange decisions
To be honest I'm not sure, don't think HUKD ever said why they were. They made the announcement back in December: https://www.hotukdeals.com/discussions/asda-currently-suspended-from-hotukdeals-3367073