I think its just a matter of your preference, but whatever you decide, make sure the door is secured from moving. We always travel with all doors secured closed.
It depends what kind you have. Sliding closet doors generally have a clip on them to hold them shut. My 303 has hinged doors that have a clip on the inside to try and hold them shut, and so far everything works good.
The 337 is designed to have the two sliding doors secured in the open position when traveling. We may put a latch on that is similar to the one on the shower doors so we can travel with them closed.
Originally we had plastic straps that held the LHS door closed and the RHS door open. I've removed that set-up and travel with the doors closed with a small bungee cord around the two door handles.
Our 337, like the others was designed to travel with the doors secured open...not so much secured though, the little plastic straps never work and after every travel day, the doors have gone rouge! I installed a small magnet latch to hold the doors closed during travel, and plan to install handles on both doors (to match all the others in the rig). Once these are in, we will simply use a small bungee to secure them during travel.