“Perhaps, but we must be diligent about our faith to “show ourselves approved”... before God.”
Yes, but this refers to studying the Scriptures.
“We are peculiar because God’s holiness separates us from the ways of the world that lead unto death..”
Yes, but you are assuming things that are not true in this case.
Timothy, and those in the position of Timothy, were to show themselves approved unto God, by turning others, over whom they possessed influence, from the pursuit of vain and unprofitable things. (From Ellicott)
You cannot show yourself approved unto God unless you rightly divide the word of Truth.
Only when you can properly handle the word, can you have discernment about deceptive religious practices such as yoga.
Like I said on another thread, avoid the problem altogether with Pilates.