LA and SoCal is such a melting pot of people who migrate here from all over the USA that people hold on to hometown alliances but what I have found is that they do root for the Rams except when their team is in town.
At one time in the 40s, 50s and 60s there was a home town feel for the team when they were entrenched as the only or first major league sports team in LA and had enjoyed many great teams, championships and seasons but the move to Orange County hurt them with their long time fans and then the Raiders moving here split up the loyalties and hurt both franchises actually. Plus while many like Carroll Rosenbloom who was seen as a owner who wanted to win his widow was not viewed in the same light.
If they can establish a winning tradition much as the Dodgers and Lakers and Kings have done then they will get more loyal fans.
Grits