You usually need PS Plus to play Red Dead Online, but by May 27th, that will not be necessary.
It was announced on PS Blog that as part of a special period, all PS4 players will be able to play Red Dead Online without a PS Plus subscription. The special season coincides with the update that ended the beta period.
Yesterday’s update brought several new features such as new characters for free roam, new types of missions, increased amount of gold you receive, and new activities such as fishing, bird hunting and picking herbs.
You can read everything about yesterday’s update here.
There is no similar offer on Xbox One. If you want to play Red Dead Online, you’ll need the same subscription to Xbox Live Gold.