I always end the game with all my civics across the bottom: Universal Suffrage, Free Speech, Emancipation, Environmentalism, Free Religion. When I switch to these and why:
Universal Suffrage - when I'm far enough ahead in tech and the build from the hammers in towns plus being able to buy rush becomes more important than the three extra research points per specialist of Representation. Very late, usually.
Free Speech - immediately on reaching Liberalism. No reason not to, really.
Emancipation - immediately on reaching Democracy. Very good reasons TO, I think!
Environmentalism - when my cities are getting so big that they're going into bad health no matter what I do. That's especially important in BtS, where unhealthiness with big pops seems to be worse than it was in vanilla. DO NOT blow off bad health! Bad health = slowed growth, plus you lose some production and commerce because you have to put more people into producing food to compensate. Big cities = more specialists, a good thing. So the answer is, pretty late, but not as late as U.S.
Free Religion - as soon as I finish the war I'm either building towards or in the middle of fighting every time I hit Liberalism. Until then, I stay with Theocracy for the better troops.
BTW I think maybe that need to compensate for lost food is the reason why switching to Environmentalism is often a moneymaker (unless you do it earlier than you should).
Everyone should bear in mind that Sid is himself a raving greenie, as anyone who's played Alpha Centauri can attest. So naturally Enviro is going to be a very good end-game tech.