I would argue yes, as soon as is practical. Many people have forgotten that our military presence in the Kingdom starting in 1990 with the Persian Gulf War buildup were the major reason why we were attacked in subsequent years by al-Qaeda, including September 11th. Our presence in the Muslim holy land has radicalized tens of thousands of people and continues to damage our reputation in the Arab world.
What's more, it isn't necessary in the long term. Our initial deployment there was to protect against Iraq, not Iran, and even with that threat we are still able to pre-position American military equipment there should an emergency arise.
Iran is a fairly weak state economically and otherwise, and even if they were to obtain a nuclear weapon, no amount of American troops would protect against that.
I would argue that removing all US military forces from Saudi Arabia would be a bad idea at this point. I will mention three reasons for this.
- Oil. We are very dependent on oil from the Middle East and from Saudi Arabia in general. This oil runs the world's economy and it is in US interests to protect it as it did during the Persian Gulf War of 1991.
- Iran. Iran is an enemy of the US and of Saudi Arabia. Removing US forces from Saudi Arabia would strengthen Iran.
- Our alliance with Saudi Arabia. We have very few solid allies in the Arab world. Saudi Arabia is by far the most important one we have. As long as they want our forces there, it is in our interests to leave the troops so as to maintain our relationship with the Saudis.