General relativity allows for multiple different kinds of wormholes just as there are multiple different solutions to the field equations.
Wormholes fall into two major categories, non-traversable and traversable, the latter requiring a lot of caveats.
Non-traversable wormholes are solutions that are intrinsically unstable where the wormhole - if it forms - collapses faster than something can travel through it at slower than light speeds with respect to the wormhole metric. Since you would need to travel faster than light to traverse the wormhole, this is explicitly forbidden by relativity.
The idea of a traversable wormhole is based on meeting a number of different requirements such as not having to cross into or out of an event horizon, survivable tidal forces, slower than light metrics, etc. These are usually called Morris-Thorne wormholes. Wormhole metrics that meet these conditions have been formulated and would be traversable and survivable IF the metric can in created.
All metrics in general relativity must have associated matter/energy distributions that create the metrics while still satisfying the constraints of the field equations. This is where the rub comes in from a theoretical standpoint with the so-called traversable wormholes. The matter/energy conditions require negative matter/energy which is not known to exist. So, technically these are theoretical solutions if the matter/energy conditions can be met, but since we know of no way to satisfy the conditions it is somewhat dubious to say the they are theoretically possible. It should be noted that negative pressure can exist, and could in principle satisfy the negative/matter energy condition, but it is only known to exist in minute quantities associated with vacuum energy.
So, at this stage of our knowledge, we can probably conclude that nothing prevents non-traversable wormholes to form but since they would instantly collapse It’s somewhat meaningless. We could also probably conclude that traversable wormholes - if the negative energy condition could be met - would not form naturally. However, we would still have to allow the possibility that a sufficiently advanced civilization could create one if the negative energy condition can be satisfied.