After reading this article, I couldn't help but hook myself up to the biofeedback monitor to get the blood pressure back under control. 

Here are the arguments put forth against local homeschoolers participating in public school sports programs (one of the few things public schools actually do pretty well):

1. Coaches will game the system by recruiting top players -

My $0.02 - the NCAA deals with these activities all the time and the same policies will work at the high school level.

2. Allowing homeschoolers to play for local teams would devastate eligibility and participation requirements

I could only find 9 eligibility requirements on the VHSL Participation form, but perhaps the rest are health-related - here they are: 

• must be a regular bona fide student in good standing of the school you represent. - Duh ...
• must be enrolled in the last four years of high school. (Eighth-grade students may be eligible for junior varsity.) - No reason why this cannot be enforced with homeschoolers.
• must have enrolled not later than the fifteenth day of the current semester. - No reason why this cannot be enforced with homeschoolers.
• for the first semester must be currently enrolled in not fewer than five subjects, or their equivalent, offered for credit and which may be used for graduation and have passed five subjects, or their equivalent, offered for credit and which may be used for graduation the immediately preceding year or the immediately preceding semester for schools that certify credits on a semester basis. (Check with your principal for equivalent requirements). May not repeat courses for eligibility purposes for which credit has been previously awarded. - No reason why this cannot be enforced with homeschoolers.
• for the second semester must be currently enrolled in not fewer than five subjects, or their equivalent, offered for credit and which may be used for graduation and have passed five subjects, or their equivalent, offered for credit and which may be used for graduation the immediately preceding semester. (Check with your principal for equivalent requirements.) - No reason why this cannot be enforced with homeschoolers.
• must sit out all VHSL competition for 365 consecutive calendar days following a school transfer unless the transfer corresponded
with a family move. (Check with your principal for exceptions.) - No reason why this cannot be enforced with homeschoolers.
• must not have reached your nineteenth birthday on or before the first day of August of the current school year. - No reason why this cannot be enforced with homeschoolers.
• must not, after entering the ninth grade for the first time, have been enrolled in or been eligible for enrollment in high school more than eight consecutive semesters. - No reason why this cannot be enforced with homeschoolers.
• must have submitted to your principal before any kind of participation, including tryouts or practice as a member of any school athletic or cheerleading team, an Athletic Participation/Parental Consent/Physical Examination Form, completely filled in and properly signed attesting that you have been examined during this school year and found to be physically fit for athletic competition and that your parents consent to your participation. - No reason why this cannot be enforced with homeschoolers.
• must not be in violation of VHSL Amateur, Awards, All Star or College Team Rules. (Check with your principal for clarification in regard to cheerleading. - No reason why this cannot be enforced with homeschoolers.

3.  There is little or no periodic monitoring of academic progress for children taught by parents at kitchen tables, unlike in public classrooms. - Heard of SAT testing?
4.  There is no way to verify that a student is doing classroom work through the day, instead of working out with a personal trainer. - Heard of SAT testing?
5.  It would foment resentment among students and athletes, their parents and particularly school faculty. - Huh? See the next item.
6.  "The teachers are going to have that message ringing in their ears: 'I'm not good enough to provide you an education during the day, but I'm good enough to provide you come and play.' - OK, now I understand #5. Here's a solution: "Grow up"

So it seems to me that the argument against homeschoolers' participation is mainly a form of "finger in the dyke" solution for teachers unions to bully homeschoolers into public school attendance.