-Techs can be dead ends or unneeded for certain paths. It seems I can skip Theology (and Divine Right) altogether on a Space Race. What other techs may be skipped in certain situations?
It depends somewhat on what your trading strategy is, and A LOT on the difficulty being played. I play almost exclusively on low difficulty because I suck (Noble, Prince) and things like Aesthetics trade and skipping Alpha for the AI to get instead work terribly, as the AI doesn't have its cheater economy bonuses down here. Read a lot of the advanced player's write-ups here or watch games from AbsoluteZero/TMIT on youtube, and you'll see this stuff work fantastic up on Immortal/Deity though. On lower difficulty you can actually self-tech any path you want to, whether going for war, wonders, or space, both because you have to (trade-bait is horrible as the AIs are slow as molasses) and because it's possible to outdo the AIs very quickly and never look back if you tie them up in diplomatic wars or go for an early war to conquer a couple of them.
In general, I find I can ignore 100% of the time:
-Drama
-Divine Right
-Mass Media
-Flight
-Advanced Flight
-Stealth
-The Astronomy line on Pangaea/Inland Sea maps.
-Military Science
No matter how long the game goes, or what victory type I go for. Drama is never important early unless you want a GT+HE city for heavy unit whipping, and you can always trade back for it later for Cultural Victory long after it's already long beyond worthless. Divine Right is one of the least useful techs in the game except for holding it over the AI as a trade chip, when you should instead be focusing on the run to Lib (I can get mild use out of its wonders for fail-gold abuse with IND leaders though). Mass Media has nice cultural wonders that you never need, and you can leave the AI the task of building the UN, it doesn't matter who does it. I don't like bombers, prefer nukes instead, and their techs aren't required for the Space Race. Stealth would be more appealing on non-Pangaea/Inland Sea maps where a powerful late game navy is desired, but again, nukes. Navies are very hard to justify on these maps at all and while I might not necessarily never trade for the Astronomy line if I have lots of coastal cities (for the extra trade from Harbors/Custom Houses), it's never a priority. I know Grenadiers are a good counter to Rifles if you are behind, but would rather go Cannons 100% of the time unless I was totally incapable (no iron).
Techs I usually never tech myself, but may trade for if it suits me:
-Polytheism: ToA sucks, don't care about religion founding
-Monotheism: OR isn't worth teching it myself, and even though the AI values it highly, they are dicks about trading anything for it fairly.
-Monarchy: even without the Mids, I just have too many other important things to tech. Tradeback if I *need* HR civic, but can normally wait as trading for their Wine works too.
-Iron Working (this is actually usually a priority trade after self-teching Alpha)
-Theology: If I want to build the AP in a throwaway religion, or if playing for an AP victory goal and got beat to it somehow. Theocracy also makes a lot more sense for war than Vassalage if you have good religion spread most of the time, instead of giving up Bureau/Free Speech/Nationhood.
Techs I PREFER to have the AI research for me, but still important:
-Code of Laws
-Feudalism
-Banking
-Replaceable parts (PP is too important to wait for)
-Artillery
Then there's a bunch of stuff that just gets self-teched or traded for as opportunity presents itself, but it's never a major thing to wait or have to do it yourself either way. Stuff like Fishing, Sailing, Masonry, Metal Casting, Machinery, Guilds, Gunpowder, etc. You will need all this stuff eventually, one way or the other, but unless going for a specific rush strategy it won't kill you to pick it up later as you can, instead of prioritizing it. Nationalism, Printing Press, and Military Tradition fall under here, but are usually prime Lib targets because they lead into Cuir/Cav wars or speed up Rifling.
What's left is either too important to put off (stuff like worker techs, Currency, Liberalism if you don't cede the race), you lose too powerful an advantage if you wait to tech it (wonder techs, war techs), or the AI is simply way too stingy to trade it/trade for it freely due to nothing more than the turn progress--for instance, they simply refuse to trade Construction even if they like you, they don't even have a monopoly, and you have put several turns into it, if it is "too early" in the game due to the way they value certain techs (Construction being one of these). Their refusal to trade along with their poor tech rates on low difficulty basically means you have to tech it yourself if you want to get any good use of it in a decent time frame, and nixes a lot of trade-bait teching strategy like the Aes line. So if your plan was early war because you have access to Ivory, you are much better off planning on self-teching Math->Construction yourself, and by the time you do this they usually are ok with trading HBR which they otherwise value very highly in the early turns. For the same reason, self-teching Alpha before Currency is much better down on Noble/Prince, because if you don't you'll be waiting
even longer to backfill techs that you actually want that they may trade by then (like Iron Working or HBR).
But religion is nice - can make multiple sides of world... and you... stay alive between them all but never be clear 1st target (with some help to smaller guys to keep wars going without capitulation)... with single warrior per city up to industrial era 
