In many ways Israel does the US' dirty work, like crippling Hezbollah which is responsible for numerous attacks against US (and other Western) personnel.
The Houthis are squarely to blame for the disruption of Red Sea shipping; Israel's military operation in a different country isn't a legitimate reason to attack (almost) random ships.
Many in the U.S. feel that protecting Israel is a moral cause, but it is undeniably a strategic albatross for us.
No, another is that they are proxies of Iran, which the US has problems with that go beyond attacking Israel.
You can't know that. The Iranian Islamic revolution happened not because of Israel. Iran would have probably tried to gain influence through proxies and destabilize the Middle East regardless of Israel. It would have joined forces with Russia and China. It would have probably tried acquiring nuclear weapons and it would have hated the U.S (which it calls Big Satan to this day). In short Iran would have been a huge headache and security risk for the U.S and the West even if Israel didn't exist imo. The U.S is definitely strong enough to deal with Iran without Israel, but its helpful to have allies in a very very unstable neighborhood.
Israel provides us zero military bases, even when Arab countries provide us dozens. Despite all of the support we give them and have given them, they have repeatedly escalated conflicts when the U.S. asked them to stop. Today, we are unable to ship goods through the Red Sea because the Houthis are upset over Israel’s actions in Gaza.