The reason it's not practiced today is 'just' because the decree also states that you have to perform the sacrifice at the great temple on temple mount. That poses a technical problem, since: 1. The temple was destroyed 2k years back, and there's a pretty famous mosque standing in its place. 2. Religious jews have to do a special kind of purification in order to even be on temple mount, and this purification is impossible at the moment, again for weird technical reasons (they need a red cow, don't ask).
BUT, if there was a temple, and there was a purification rite, religious jews would, in all likelihood, be happily burning offerings 3 times each year.
In short, not as different as you may think.