Sorry if some of these are repeats, but these schools all have natural grass:
3A - West Vigo, Greencastle, North Montgomery, Indianapolis Washington
2A - Monrovia, Seeger, South Vermillion, Speedway, North Putnam, Alexandria, Eastern (Greentown), Elwood, Alexandria
1A - South Putnam, Anderson Prep, North Central (Farmersburg), the entire WRC (Fountain Central, Covington, Parke Heritage, Riverton Parke, North Vermillion, Attica) School for the Deaf, Cloverdale, Madison Grant, Tri-County, Clinton Prairie, Clinton Central
I don't know if they still do but Covenant Christian used to play their home games at one of the Zionsville Middle Schools which is a natural grass field. To my knowledge, they do not have their own home field.