People with disabilities can and should be allowed to participate in sports. The benefits received from sport (physical fitness, social inclusion, community integration) make it hugely disadvantageous to an individual to not let them participate. The right to play sport is not about making sure a person with a disability competes outside their level of ability, it's about giving them the opportunity to compete at a level where they can be a competitive player.
Individuals who are disabled have the right to engage in sports. There may need to be certain accommodations made to compensate for their disabilities. For instance, the Special Olympics is intended to develop and acknowledge the athletic ability of individuals with disabilities. To say individuals with a disability does not have the right to participate in athletics is not fair.
While we should encourage everyone, including disabled people, to get involved with sports, it is certainly not a civil rights issue. Many sports teams are built around a specific level of play, and if you cannot match that, whether you are disabled or not, you may not be able to participate.
The only civil right at play here is the option to be able to do something. The idea that certain sports should change to accommodate particular disabilities is crazy. If someone physically cannot run, should we change track and field to accommodate them? No. Should we allow them to try, if they wish? Yes. That is the only issue here. If someone with a disability wants to try, then they should be allowed.
We shouldn't ban people with disabilities from competing in sports if they are able to compete on the level required despite their disability. But engaging in sports should not be considered a civil liberty. As everyone else, I have handicaps to what I am capable of doing in life, and it would be absurd for me to claim that I have a civil liberty to do them anyway. It amounts to the idea that everyone should have equal opportunity whether they are competent or not. This is not to say that there shouldn't be avenues for disabled people to compete in sports, just that it is a slippery slope to say they have a civil right to do so. We would have to address everyone's right to do anything they wanted whether capable or not.