The Githyanki and Githzerai are warring factions of the same species, Gith.
But after they won their freedom, two factions among the gith disagreed on what kind of civilization they would forge.
These factions are later described as the Githyanki and the Githzerai.
Further, MToF lists the two as subraces of Gith. No matter which you choose to play, the race details state, “Your character shares the following traits with other gith”, then goes on to detail the specifics of each subrace.
The confusion is understandable, twice in MToF the two are referred to as “two races”, but I do not see any reason to believe that the Githyanki and Githzerai are different races in such a way that their biology would be so fundamentally different that one would lay eggs and one would not.