Many rescues do spay and neuter their animals before adopting them out.
Metropolitan Guinea Pig Rescue is an example of this. Unfortunately, there are not many vets that are trained to safely perform these operations or do not do them on a regular basis. Because of this, the shelters and rescues will make sure that the animals are at the very least accurately sexed, and require adopters to sign legal contracts that they will not breed the animals being adopted. Usually, they will only adopt out as a friend to a same sex animal or another animal that has previously been altered.
Being competently skilled at spaying a dog or cat is routine.