I somewhat disagree from @chaqke answer. I'll explain why.
 What I wish to know is, what method is used to balance StarCraft with respect to Protoss' ability to do aggression and harass?
Sc2 gets some new balance patches when the state of the game seems to favor one or another race. Speaking about the latest notes released by David Kim and his team, Protoss' Adepts seem to be too strong in early game vs Terran.
So, since everybody reported that thing happening, adepts will be most likely nerfed in the next patches.
 Is it objectively true that a Protoss can't be as good at aggression and harass compared to a Terran?
In my opinion, no, absolutely not. At the current state of TvP, Protoss has huge harassment power.
- Opening with Adepts -> Scouting, Get rid off Reapers, Forcing Terran to Bunker Up, Protoss has map control, Upgrading Adepts and drop them with 4/5 gates
- Opening with Oracles -> You can punish greedy opponents and block the first pushes
- Opening with Phoenixes -> Protoss has map control, Terran drops denied, Forcing Terran to build turrets/WidowMines/Cyclones, denying Liberator Harass
- Other non popular openings: Based on DT drops or similar, not really early
- Reaper opening -> Scouting, getting maybe 1 probe, killed by an adept or Pylon Overcharge
- Cyclone opening -> Map control, killed by Blink Stalkers or Phoenixes
- Widow Mine Drop -> If no robo opening and no Phoenixes opening it's very good, in the other cases its basically a lost game
- Banshee opening -> Way too easy to scout for Protoss, probably getting killed by Phoenixes or a well placed Pylon Overcharge
- Liberator Opening -> Pretty cost effective, maybe getting 4/5 probe kills
- Fast bio drop -> Gets killed by Adepts, Pylon Overcharge or Similar
- Fast Tank + Bio Drop -> Pretty cost effective, gets killed by Phoenixes openings or good Toss Micro
So, basically, if Protoss opens with 1 or more Adepts and Stargate it's pretty safe and also can make a mid game all'in or attack focused on Adept/ChargeZealots Warp Prism drop (Very popular).
 Is it merely that most Protoss prefer to play defense, and simply haven't explored other aspects?
I don't think so, if you watch high level korean players, they already know how to harass in early-mid game. You can also play defensive, but playing a bit aggressive, if well done, always pays off.
 For two equally skilled pro league players, one Protoss and one Terran, would the Protoss always perform worse than the Terran using aggression/harass tactic?
Absolutely not. It depends on the skill of the players involved in that game. But, for the actual state of the game, I would put my bet on a better Protoss' harass.
 Could there possibly exist a pro league Protoss who plays an aggressive/harassment Terran-like style and still do well enough to win tournaments?
I can name Parting, CJherO and Zest. Of course, the harassment is done differently from Terran's harassment but these guys know how to poke their opponent for sure. MC is not playing tournaments anymore, but he's also capable of doing that.
In my opinion, by now Protoss is winning on that aspect on Terran, I'm an experienced Master Protoss but it's still my personal opinion. If you want to get started with some serious harass, take note of what I written over and watch some serious Protoss Streamers that stream often:
Now, in response to @chaqke opinion
I somewhat agree. Ok, speaking about TvP, the reaper is the fastest unit in early game. But at the current state of the game, Protoss is way too far better than terran because of adepts. Every Protoss is opening with adepts. They are strong vs bio and they can chase reapers easy and kill them with few Shots. If you want to get rid of Adepts you can:
- Build a bunker and a barrier -> Protoss has map control
- Go for Cyclones -> Not really ideal against most of Protoss' units
So, In my opinion, Protoss is way better in early game.
I agree but mid game all'ins with prism (Charge Zealots and Adepts) are very strong and easy to do.
I agree but in my opinion Oracle is a really powerful tool. Phoenixes are really a thing in the current meta. They allow you to repel most of the early pressure, harassing, forcing wrong units and taking map control.
I somewhat agree. As explained before, reaper can be fast, yes, but adept really counters it properly. Speed is an important thing, yes, like boosting your medivacs or just stimming some bio into far away opponent's bases. But, maybe Charge Zealots, Adepts and DTS are not that fast, but they can harass in a really cost effective way and you don't need to pay as much attention on them as the Terran does with its drop.
I agree, but you have also to mention Disruptor and Oracle Revelation for Protoss. Revelation gives both Disruptors and Tempests a really powerful harassing/attacking power.
I hope I've been helpful, GL & HF.