How many damage types is optimal for a build. I’m currently playing a Purifier (Inquisitor + Commando) and using Lightning and Fire, with Stun Jacks for crowd control. But I’m wondering if using two damage types will hurt in the end.
I think two damage types, especially for that build are OK. Both are elemental and supported by both masteries.
1 damage types is perfect
2 damage types is also good
3 damage types if you are really know that you do and how it will works
4 damage types is no, just no
Less is more 
Generally the builds that have the fastest crucible times will be tweaked to get as much damage as possible out of them. That’s generally easiest to achieve when you focus relentlessly on just one damage type.
But you can do nearly as well with two types, especially ones that have some synergy, like fire and chaos, from skills and items. It also helps with enemies that have stupidly high resist for your one damage type (void leeches and vitality, for example).
I wouldn’t go beyond two however, efficiency really drops off at that point (exception is elemental, technically three types but rolled into one).
The only disadvantage of limiting to one damage type is that mobs highly resistant to it can be a pain (ex. cold damage against yeti’s or aether vs port valbury boss guard starfire).
Most damages however come quite nicely into pairs without giving up too much damage on either.
In my opinion, if you can support two types at once (e.g. Physical and Aether, Fire and Lightning, Chaos and Vitality) then it won’t hurt. Some build (maybe even most of them) can focus on only one damage type, though. You should always go for a main damage type, for example fire and if you can support some lightning damage with your build and class, you may (but don’t have to) go for lightning too. The most important thing is resist reduction, if you can get elemental RR or both, fire and lightning, you’re good to go, but you should remember about having a main damage type which would be mostly focused on.
Example: Krieg’s set grants both, Aether and Physical damage, and your weapon converts 40 - 60% physical to aether, your aether damage is 1700% and physical 1500, you can easily go for physical resist reduction in devotion as well as aether resist, and therefore you will have solid build with two damage types, which will be good vs. many enemies. There are, however, issues with that, because you sometimes (keyword) can’t focus on both, damage and defense, and therefore being solidly good in damage, but weak in defense, or weak in damage and solid in defense (or 50:50, but whatever, you get the point anyway).
I had a Physical and Aether based character, which was good, I used to hit for 390 000+ damage, but unfortunately died easily due to the lack of any defense, as I had to focus on damage in order to make my dual type build effective (I had over 1700% in both, Physical and Aether damage).
I go for two, tops
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That can actually be one of the advantages to a single damage type. You can focus on one resist reduction type so that you either get big damage boosts on mobs with little to no resistance, or completely strip the resistance from the highly resistant mobs.
The other advantage is to be able to stack damage for a single damage type.
This is true for endgame, but early-midgame when you don’t have access to RR yet, it’s a PITA killing resistant mobs if you only have 1 damage type.
Probably worth mentioning that Pet builds and also Retaliation builds are usually exempt from this and end up as amalgamations of damages types due to gearing for these archetypes often featuring % to all damage, so even if they also use specialised damage bonuses, they can make sufficient use of other damage types they do not plan for.