The title: Respecting other faiths doesn't mean compromising your own, immediately made "Christian Today" my first guess, instead of "Christianity Today", as the more post-modernist view. Mark Woods' attempt to tolerate some of the customs of other religions shows the confusion he's had with the gospel. This is a common thing in Christendom today: They can talk the talk, but they cannot walk the talk.
My response to this is simple: If you give credit to the custom of false religion, unless you do not consider them falsehood (but why give credit then?), how are you to make the true Gospel known?
Are we to just go around showing disdain to other religious customs? Hence, the opposite of showing respect. Neither. And this is the fun part, because they who can't walk the talk would be lost at this point.
This reminds me of Emperor Kangxi who suddenly banned Christianity due to the ban of Chinese rites by the pope.
What then, is the solution? Wisdom. Wisdom out of prayer. Wisdom fools will never get.