It's one of my guilty pleasures...
I usually build it because it comes with plastics, which I always beeline regardless of VC after Oxford-slinging radio. If I'm not going for a culture victory (and consequently haven't spent my 1000faith GE on Eiffel), I'll usually faith-purchase an engineer on it. Since plastics is beelined, it's usually significantly more expensive than other wonders that are available at the time (since those are 1st tier industrial wonders and Cristo is 2nd tier modern.) Also since plastics is beelined, there's enough game left for it to be compounded more than a few times...
I find it to be a win-win scenario:
1.) for tourism victories, it doesn't even shave a turn off of policy/tenet times because I'm usually getting a policy more than once every ten turns. However, it has a base culture yield of 5, 8 if cultural heritage sites has been passed (which, on deity, most of the other civs love to propose or gets you a positive diplo modifier if you propose it.) That translates to an extra 2.5 tourism (or 4 with Cultural Heritage) with hotel, 5 or 8 with airport. And then multipliers, multipliers, multipliers! Figure +50% (7.5 or 12) with your world religion since it will be in the capital, +33% with the level 3 freedom tenet, extra civ specific percentage bonuses with borders/religion/trade route, and then doubled during Igames and doubled again after internet. So for CVs, it can acount for 20-30 tourism per turn after all the multipliers, and that increased total affects how much musician bombs are worth. All in all, it's not Sistine or Pisa in terms of effectiveness, but unlike those two wonders, it is always going to be a possibility.
2.) For non-tourism games, I'm usually getting a new policy every 12-20 turns, which means that Cristo is knocking 1-2 turns off of policy/tenet times, and the +5 culture isn't game breaking but is nothing to scoff at either. And again, since I (we?) go for plastics so early, there's often enough time left in the game for it to affect at least 5, maybe as many as 10 policies.