Usually those opposed are Christian fundamentalist extremists who see yoga as competition to their religious beliefs, even though most types of yoga as taught in America are non-spiritual. They feel their religion is threatened and don’t want any competing influences in public school that may oppose their beliefs. I think the same thing happened a year or two ago in the San Diego area.
update: same place, actually: http://www.sandiegouniontribune.com/news/2014/apr/23/student-yoga-program-stretches-out/ “…attorney Dean Broyles, president of the Escondido–based National Center for Law & Policy, argued that the very act of practicing yoga could lead to interest in Hinduism and other Eastern beliefs.”
““This is frankly the clearest case of the state trampling on the religious freedom rights of citizens that I have personally witnessed in my 18 years of practice as a constitutional attorney,” Broyles said.” 4/2014 http://www.sandiegouniontribune.com/news/2014/apr/23/student-yoga-program-stretches-out/
"The National Center for Law & Policy is a conservative Christian non-profit law firm that “focuses on the protection and promotion of religious freedom, the sanctity of life, traditional marriage, parental rights, and other civil liberties.”  Its president is Dean Broyles. https://en.wikipedia.org/wiki/National_Center_for_Law_%26_Policy