They certainly should have just any neutral, because that's the most flexible choice that embraces all versions of the Githzerai from all editions. Also Monks aren't necessarily lawful only. 5e allows one to play "Taoist" or True Neutral martial artist mystics.
I really think they need to stop emphasizing the Monk thing with Githzerai, they aren't a single class race or a race of hats anyways. Other aspects of the Githzerai that should be emphasized on this fiercely individualistic race include things like, the Anarch's Guild or the Shapers.
The guide from Planes of Chaos which specialized in shaping reality to their thoughts. Something that comes easily in Limbo. Here an Anarch can be either one who's trying to impose order over chaos with their thoughts (lawful), or an artist who wants to push the limits of what they can shape more motivated by whims (chaotic) or anything in between those two. The origin of the theoretical psionic discipline of Metacreation, can be traced back to the Githzerai's Anarch's Guild.
Another side of the Githzerai is the scholarly and experimental side. As a race that often becomes Wizards or Psions, this should be emphasized too. That they are a people very much interested in understanding more about the reality and pushing the limits more. Much like that Githzerai scholar I seem to remember from Tales of the Infinite Staircase who spent everyday in a different form, or those Githzerai scientist who made some sort of psi-bomb that turned all the Githyanki in the Athas outpost into a bunch of primitive savages.
Both of these other aspects of the Githzerai should exist alongside the monastic Githzerai. And before anyone uses Dakkon as an example of the Githzerai and their philosophy as a whole, just remember that the Circle of Zerthimon in Planescape: Torment, was actually a lie created by the Nameless One himself.
