A net is a thrown weapon with a range of 5/15. This means that at 10 or 15 feet, you throw with disadvantage. However because of the Ranged Attacks in Close Combat rule you also throw at disadvantage at 5 feet (PHB, p. 195):
... When you make a ranged attack with a weapon, a spell, or some other means, you have disadvantage on the attack roll if you are within 5 feet of a hostile creature who can see you and who isn't incapacitated.
Crossbow Expert (PHB, p.265):
Thanks to extensive practice with the crossbow, you gain the following benefits:
- Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
So, does this mean that Crossbow Experts are the only PC's who can throw a net without disadvantage?