In 2023 we lived part of the year in another state. We became residents of Florida in Oct. of 2020. Why is it saying the date cannot be before 1/1/2023 in My Info?

The tax return looks at only the current year.  You can use 01/01/2023 as the date you were a resident in Florida (FL) and then the move out date.  The state is only concerned about the current tax year residency to determine your taxable income in your new state.

But if you have a vacation, or summer home in another state that you occasionally spend some time at, then you do not indicate that you moved to another state during the year.  A move to another state, is only indicated when you move your primary residence (and the majority of your stuff, and car registrations, and voter registration) to a different state.