Full-time Florida resident, substitute teach in Ohio, receive OH wages. How do I get TurboTax to recognize my non-residency and not require OH residency dates on SD 100?

Make sure that your Florida residency is correctly reported in the software.  In TurboTax Online, 

1. Select My Info down the left side of the screen.
2. Select State of residence as Florida.
3. Select Other state income as Ohio.
4. Select State Taxes down the left side of the screen.
5. Select Ohio as a nonresident.

You are a resident of a school district if you are a resident of Ohio and your primary residence is in the school district. 

Items such as your voter registration, driver's license and vehicle registration can help determine your primary residence.

This Ohio Department of Taxation website states:

Any individual (including retirees, students, minors, etc.) or estate that receives income while a resident of a taxing school district is subject to school district income tax. 

Individuals who work, but do not live, in a taxing school district are not subject to the district’s income tax.

To determine which school district you live in, as well as its tax rate, enter your home address into The Finder.

See R.C. 5748.01(G) and (H).

Contact your employer about being assessed the school district tax.