I arranged for a private half-day guided tour of Bethlehem in November of 2019, which included not just the Church of Nativity, but also a drive through the governorate countryside, several viewpoints, a visit to the Shepherds Field, and a stroll through the center of the town of Bethlehem.

Church of the Nativity itself is not unlike the Church of the Holy Sepulchre in Jerusalem, in that it is a major pilgrimage destination that is shared by several Christian denominations. The Bethlehem church is less of a madhouse, though; the stream of visitors is steady, but nowhere near the volume you find at the Holy Sepulchre. You can view the remains of the floor mosaic of the original church from the 4th century, and descend to a number of secondary grottoes where you may even have the space to yourself. With the Nativity Grotto, I profited from having a local licensed guide by being allowed to enter the cave on the “exit” side, thus bypassing the long line of pilgrims who wait a couple of hours to be able to get close for just a few seconds to the spot where Jesus was reputedly born.

This is obviously a place much more meaningful to devout Christians than it is to any secular person or otherwise non-Christian. I don't believe the church is exceptional on its own merit, and its obvious from reading the inscription that the recognition is based primarily on the church's symbolic value to the Christian world. Your mileage may vary in regards to whether this raises to the level of OUV.

Private guide is clearly the expensive option for visiting Bethlehem; there are options with Israeli guides and Palestinian ones, and if you have concerns about the safety of crossing into Palestine in general, having a local guide may help alleviate those concerns. There are also plenty of group tours daily from Jerusalem or Tel Aviv. But technically, you can visit Bethlehem on your own by crossing Checkpoint 300 to the south of Jerusalem and then hiring one of the many taxis that wait for customers on the other side.