In reply to im off:
A few bits of advice that might help.
A spondylolisthesis (especially with lower degrees of translation) really isn't life limiting. Sometimes they do show up incidentally, so there's is no guarantee what was seen on your MRI is the sole cause of any back pain.
You mentioned you've seen a neurosurgeon, which is an interesting pathway (would expect you to have been seen by orthopaedics). You didn't mention any leg symptoms, which would be the only parameter for considering surgery. If it's localised low back pain, surgery isn't an option and I'd be curious as to why this would be advised. A spinal fusion is fundamentally a huge, life-changing surgery.
As for exercise, your physio should have you doing lots of flexion-based strengthening work. This will see you right. The worst thing you can do is lessen the physical activity you do. A finding such as yours isn't a trigger to be less active, if anything it's quite the opposite.
As for climbing, generally positions of extension would be discouraged. So this might be avoiding sustained steep, overhanging routes or really steep roof problems that require a lot of extension just for the time that your back is sore. Though this shouldn't be ruled out if you progress well with the strengthening work. But other than that, it shouldn't impact your climbing.
Hope this helps and all the best for getting up and running.