What was the status of Half-Orcs as playable characters in 2e?

Question

The AD&D 2e Player's Handbook did not list half-orc as a playable race, unlike 1e.

However, half-orcs in the Monstrous Compendium are listed under orcs with class and levels limits if players want to play them. Furthermore, some adventures like Doom of Daggerdale (Wikipedia link) have NPC half-orcs with full statistics, something restricted to playable races in 2e.

What was the real status of playable half-orc characters in 2e?

Answer 1

Half-orcs, as well as many other playable races, are covered in the Complete Book of Humanoids in 2e (and then again later in Player’s Option: Skills & Powers). Historically speaking, people certainly played half-orcs in 2e times, with DM approval.

Answer 2

The AD&D 2e Dungeon Master Guide provides for this.

In Chapter 2 ("Player Character Races") of the AD&D 2e Dungeon Master Guide, after the discussion of the standard races available for PCs you find the Creating New Player Races section.

The races listed in the players handbook are only a few of the possible intelligent races populating the worlds of the AD&D game. Adventurous DMs and players may want to experiment with characters of other races, such as orcs, lycanthropes, ogres, lizardmen, or even dragons. Before you do this, however ...

The DMG goes on to outline four basic constraints:

1. The race should be humanoid (two arms, two legs, hands and feet, etc.).
2. The race cannot possess special abilities (like a brownie or a dragon)
3. The race cannot be extra-dimensional.
4. The race must be cooperative and willing to interact with the human world. (Examples of duergar and satyrs as bad candidates are offered).
   {And then it says this (to the DM)} : You must judge this criterion based on the conditions in your game world.

AD&D 2e default assumes that the DM is the world builder.

It then goes on to say:

If the conditions are met, the race can be considered as a possible player character race. Some examples of races that definitely fit the profile are half orcs, orcs, half ogres, lizardmen, goblins, centaurs, and kobolds.

The DMG then goes on to provide some guidance on ability score bonuses and penalties, as well as some guidance on class limitations as needed.

Bottom Line

The player who wants that option for a PC race needs to work with the DM, or get from the DM what a half-orc PC has as compared to the standard races in the PHB. (It's not that hard to implement, if one follows the DMG's guidance).

As with the general case for TSR D&D editions, the "there has to be a rule for this" mindset is absent.

Players Options, Skills and Powers

If one is using the later AD&D 2e material (which some people refer to as AD&D 2.5e though that's hardly official) then the Players Options volumes have some more detail. In Chapter 3 of Players Options Skills and Powers, Tables 13 through 17, various humanoids are included along with humans and demihumans, and this inlcudes half orcs.
(Thanks @mxyzplk for the reminder to check that).