Huh.
Apparently this new non-Islamist parliament only came into being about 2 weeks ago.
The Islamist parliament is the old one that was elected right after the revolution but has refused to step down.
That's why I was confused. The Islamist parliament used to be the official parliament. In fact, it was the Islamist parliament that elected the Prime Minister of the non-Islamist government. Still following?
This is a pretty big development. Previously Hafter was outside the government. Now all the forces opposed to Hafter have left and set up their own government. It sounds like it's more confusing but actually in a way things are becoming much more polarized and simple.
The new parliment was elected in June, that it only assembled recently doesn't make it less legitimate, its a natural effect of the state of the country.
If a parliament refuses to step down after an election, it may
use to be the official parliment, but it isn't any longer. Furthermore most of the secular members of the Islamist parliament has withdrawn, so its the Islamist majority of the former parliament acting as if they are still the legitimate one.
The "Islamist parliament" is only official, if you by official mean the one that controls (or rather is backed up by) the most efficient fighting machine.