I think it's a more accurate change (I think "freedom of spiritual belief" is more accurate), as there are many people who have certain sets of beliefs and practices that don't fall into any established, organized, and officially recognized religions. Religions are organized, standardized, and often bureaucratic. Beliefs, however, are fluid, and very personal, and always differ person to person, even among those of the same church. The differing beliefs may not be obvious at first, but once you look in deeper (and people stop lying to themselves about what they truly believe), there are differences.
For example, I take my beliefs from many different sources. I have yet to hear of an established belief system that I completely agree with, so I have no choice other than to draw from many different sources to construct my beliefs. Therefore, I have no actual "religion," but I have a set of beliefs. I don't necessarily worship anything either, as I don't really pray or anything like that.
There are also those who have no religion at all, so saying "freedom of religion" would be inaccurate in the first place. Everyone, however, has beliefs, whether related to religion or not.