Mandate of heaven is a very strong way to get extra culture if going for a culture win.
Free religion still gives you 'Two free policies' that do not add to your policy cost increase. If you think that neither of those are worth it, then you really dont understand the mechanics of trying to gain a culture win in Civ V.
The best way to use Reformation and Free Religion is after you have built the Cristo Redentor. You should also save as many other policies as you can until then to get the additional 33% discount.
Even with the acoustics slingshot to take free speech with as my 4th policy choice, Oracle plus Sydney Opera House, and prioritizing culture buildings in all of my cities, I only managed to get 4 full policy trees by 1950 AD, with only one policy in my 5th tree (tradition + aristocracy).
You NEED every bit of culture you can possibly get, and you need to save policies until after the Sydney opera house is built. Mandate of Heaven is crucial as well as pumping up happiness along with it to boost culture gain, as is free religion.