Okay, I can deffinately see your point in that context. A personal invitation like that might be more awkward. But when I read the article in question I thought they said it was a blanket invitation to all the staff. I must have read it wrong.
But let`s take religion out of the picture for a moment. If I were a member of PETA (People for the Ethical Treatment of Animals) and my boss invited me to go with him and a few coworkers on a hunting trip, would it really jepordize my job to say no thanks? If that kind of work environment is really prevalent back home, I don`t think religion is the issue people should be worried about.
What, do you have something against animals now? I don't get it.
Kidding. Good point, though. Seems like you're touching on unfair treatment. However, religion and PETA are two different things, not only in how morality views them but in how the law does.