Well, from the standpoint of the law, no, there is no "right" for home schoolers to participate in public school anything unless the constitution for that state is amended. There are 10 states that are Equal Access states...we ain't one of them. In those states, home school students have to meet certain requirements in order to participate on the teams. The requirements are something along the lines of meeting the requirements of any other student, passing their core subjects, and be in compliance with the state home school laws.
BTW, I have never used the word "right" in any of my arguments, not that anyone has accused me of it, but just to make sure I get that on the table.
I really don't see the big deal with allowing them to compete as a separate team as long as they meet all the other requirements that any other team meet.
Again, what's the big deal?