I don't think BR has received anything but support from LFC fans. I've not heard any dissent at matches and neither have I heard of any campaign anywhere to get him sacked.
That's not to say that some fans aren't critical in many ways and some didn't even like his appointment in the first place. If such fans can't express their opinions and discuss the matter in a place like koptalk where else can they do so? I don't see dicussing a manager, player, team selection, tacticts etc. in this way as not being behind a manager. It's just what fans do, especially fans of teams not living up to expectations.