Religion that God our Father accepts as pure and faultless is this: to look after orphans and widows in their distress and to keep oneself from being polluted by the world. - James 1:27
The word religion is used only one time (as far as i know) in the new testament. And interestingly its not used to explain all the activity we do in the name of religion. All the temple based activities are not here.
The religion that God accepts is this:
1. Caring for the weak people (orphans and widows)
2. Living a holy life
If you are doing these two things, then you are following a religion that God accepts. If not, then you are following some other religion that God does not accept.