No. If 5% of my voting base sits out over a single issue, I’m going to lose my interest in trying to triangulate their support and move in another direction to identify a more persuadable bloc of voters. That goes more if the abandonment is repetitive, and if the issues constantly change, or if the issue is something I can’t bend on for electoral reasons.
If one bloc of voters is easier to please than another, then I’m moving in their direction, even if it’s rightward. Unfortunately it’s winner-take-all, and you’re either in power or you’re not. There are no half-wins.
I directly answered your question, and you seem to have ignored what I said. Plus you really should reexamine your assumptions about the importance of Gaza, the “ease” of withdrawing support, how much Democrats have moved rightward, and how many centrist Republicans vote for Democrats.
Your level of frustration with the process is inversely proportional to your awareness of these trends, of which Democratic leaders are likely well aware. Moreover, you seem to be valuing the strongly-held opinions of voters in non-swing states (what you’re calling “deep blue states” or “areas that effectively don’t matter”) more highly than the maybe-less-strongly held opinions of voters in swing states. If 5% of Democratic voters in California want sushi, and 5% of Democratic voters in Pennsylvania want steak, I’m picking steak and telling the California voters to take a hike. Their opinion doesn’t even register on my radar thanks to the electoral consequences of pissing off the Pennsylvanians who wanted steak.