I am trying to develop an app which contains booking URLs of various third party websites. Users need to be redirected in order to access the details and book a ticket if needed.
Considering Apple is not allowing redirections for any kind of payments, will my app be rejected? Even though I am not getting paid via the URLs to be accessed?
I believe that you won't get rejected for that. Apple's statement about in-app payments are related to virtual goods and services. If you are offering physical things (ex: books or in your case any kind of tickets - theatre, airplane, cinema etc.) they do not enforce the usage of In-App purchases. I had developed in the past an app that is used for selling photo books and we used 3rd party payment provider for purchases and we didn't have any issues with Apple.
And even if you get reject for any reason, you can always appeal the rejection and explain your use-case in details to the Apple reviewer.
Best of luck!