The US could provide humanitarian aid, but not military aid. Cut military aid to Israel. Maybe still provide Iron Dome reloads, but that's about it. Bring in a hospital ship off Gaza, to care for the injured. Send a few frigates to protect it from all parties. Discourage outside interference. Then wait to see how this plays out. It's not the US's fight, after all.
Creating a lot of noise over the issue tends to force people to choose a side and eliminates middle options. That may be part of the intent of this campaign. "Are you with us, or against us". No, we're fed up with both of you.
[1] https://www.newyorker.com/news/the-political-scene/why-a-sta...
Also, if Israel takes the control of the Gaza Strip, a lot of refugees will spread in the region, creating more tension in the long-term. I deem this more sensitive than the religious strife, because it can leave concrete, direct, and explicit marks on the neighboring societies.
I think the best scenario for US is that Israel eventually stands down and falls back to the pre-war state - that is, no Israel control over the Palestinian territories. Israel won't have much choice here.
Less of an issue than it used to be. The US is now a net oil exporter.[1]
[1] https://www.eia.gov/energyexplained/oil-and-petroleum-produc...