Lets look at some concepts for those who aren't truly religious:
1.) Death is not the end but the begining:
Therefore, dying is no big deal.
2.) God has his plan and its not your job to get in the way:
Therefore, praying isn't to make your daughter better, its to hope that that is part of gods plan. If god wants your daughter dead (and thus in the afterlife) thats his business and you have to have faith its for the best.
To many very devout people (some in my family) stopping someone in your family from dying of natural causes is shameful and embarassing, showing a lack of faith in god and everlasting life. Trying to stop death from natural causes is viewed with the same eye rolling as a kid trying to stop puberty or a middle aged woman trying to stop menopause.
And this is where I get back to my earlier comment. If you are going to say everyone is entitled to their own religion you have to realize what a religion is at heart.
A vastly different way of looking at the world, down the core concepts of right and wrong, of socially acceptable and not.