Flexibility in my opinion is extremely underrated. I think being flexible can be one of the greatest tools in climbing.
I myself am not flexible at all, but my friends are, and the difference between how we climb is so noticeable. Moves that are so difficult for me are just easy to them.
You dont have to be flexible to climb, but, it would make a huge difference if you were.
There is no real rule as to how flexible you need to be for climbing, but, being flexible can really help a lot in climbing and in solving the problems. It gives you more tools to use on the wall to finish the routes.
Having basic flexibility and a full range of motion is a good starting point, and building on that can get you a long way in climbing.
If you are not flexible, though, don't think that you won't be able to climb hard routes. I have known many people who cannot touch their toes even with slightly bent knees, and they can climb v7/v8.
On the other hand, I know some climbers who are very flexible and that are relatively beginners, they normally climb v5/v6, but sometimes they are able to top some v7s due to their flexibility. It just gives them that additional advantage.
Being flexible can also help prevent injuries. Some routes require a low level of flexibility, and others may require quite a high level of flexibility. Working on routes that require a level of flexibility that you do not have could result in injury.
Being flexible in general also just helps prevents injuries.
