Is nematic ordering time-reversal invariant?

Nematic ordering is a breakdown of rotational symmetry, and does not involve breaking time-reversal symmetry. The two references you give do not contradict each other, the first just emphasizes that time-reversal symmetry is preserved.

This fact is obvious when you look at the isotropic to nematic transition of liquid crystals (where nematicity originated from essentially). Here you have the polymers start out randomly oriented, and then they order by lining up. If you just look at the phase where the polymers are lined up, nothing changes by reversing time, it is simply a spatial ordering.

Take a look at the image below, which emphasizes that nematic/smectic/crystalline transitions are simply spatial orderings.