Absolutely. Unlike the football rivalries in other cities, the Liverpool/Everton one is almost aggressively friendly (e.g. the Harry Enfield Scousers sketch "I hope *your* team win." "Yeah, well I hope your team win." "You what?" *headbuts*).
Even without that, though, most Everton supporters within Liverpool will have friends, relatives or colleagues who died at Hillsborough, and will be very sensitive to the reputation of the city. It was (and from what I can tell still is) seen as much bigger than which team you support.