You've been given great advice above
Rope or fabric is never good for budgies in any way.
Additionally, I'm sure you care a lot about your birds and give them a wonderful space to live in, a great diet, etc. But a lot of people may not think that colony breeding has significant dangers, either because they haven't learned about it or because problems have never happened to them, or both. It may be that your budgies so far have not had any issues, but that doesn't mean it will never happen. That's why it's always best to separate breeding pairs into their own cages to reduce stress as much as possible