Homeschooling is home based education meaning the parent or guardian is in charge of the education of the child. It is done at home via internet or with books and workbooks and parent led teaching. Home schools are governed by the laws of the state they are located in.
Yes. It is very much illegal. It is considered the same as discriminating against homosexuals. Not that the internet is governed very well. If you or someone you know is a victim of discrimination please contact your local police.