For a casual, achievements are completely optional. Since they are just another way to potentially enjoy the game, there is really no incentive to achieve them beyond personal satisfaction. Now some casuals might want to get as many achievements as they possibly can, and that's cool. But they likely won't fret if they can't get a black proto-drake.
The moderate is the person who chooses to play the game more seriously than the casual. He will attempt to do things that are difficult, but not put in 20 hours a week of play time just to do them. The moderate is probably in a guild and enjoys the connections he's established there.
For a moderate, I can see achievements still being optional. It's likely the moderate player hangs out with other moderate players, so if he's not caring about the number of achievement points he's likely not to face any sort of peer pressure to get them. And at that point, he's equal with the rest of the group and there is very little social incentive to advance.
The Hard Core
The hard core player is a person who strives to do the content fast, perfect, and in the hardest modes. He will attempt to get as many achievement points as necessary to not be a joke, and will at least have enough points to be looked at respectively by his peers.
Of course his peers are members of his guild, who are likely to share his view points. Thus having 4,000+ achievement points is looked at as normal, and having 5,000 or more would be seen as something desirable. This could come further into play in that if he ever wanted to switch guilds, the new guild would obviously look back upon his achievements to determine his worthiness at inclusion in their social group.
After all, what better way to tell if someone knows heroic and raids than to see if they've gotten The Immortal?
So for the hard core player, achievements are definitely not optional.
In the end, it all comes down to what social group and in-game group you're with. Casual and moderate players probably won't be faced with pressure to care very much about their achievements. Hard core players will, on the other hand, face pressure to have as many "hard core" achievements as possible.
Now it could be argued (and I personally think correctly) that this is all just a social construct by Blizzard to get players to spend more time in the game working towards truly pointless goals – and that achievements are the very definition of things that don't matter. There's some truth to that for sure, but at the end of the day, the question of "Are achievement s optional?" really comes down to what your peers thinks.
That, or your just a crabby old man who doesn't give a flyin' hoot about what other people think. /wink