My thoughts on the use of the therapy is traditional, yet controversial by many standards.
There's a little confusion as to whether we're talking about your thoughts or the use of the therapy. The sentence structure says your thoughts are controversial, but the choice of a singular verb suggests the use is controversial.
The sentence implies that different communities, or groups of people, have different opinions about the therapy. The "standards" of each group may be said to determine their views on the subject.
In communities where the therapy is traditional, it has a long history, which doesn't necessarily mean everyone approves. Or, everyone may agree that it's good and useful.
The standards of other groups may lead them to oppose it's use, or even forbid it. Or their standards may say it's controversial, which usually means some are strongly in favor and some are strongly opposed to it's use.
Traditional, yet controversial therapies come to mind, like black magic, blood letting, hypnotism, prostitution, exorcism, spanking, layatril, magnets, etc.
Edit. Arguably, some of these may be considered remedies rather than therapies. I guess I must check my definitions.