Bradford Council says plans for the outlet in Oxenhope go against its policy on takeaways.
The bridge, on a walking route near Oxenhope, replaces one that was falling apart.
An application says that the good the business will do would outweigh any concerns.
The Keighley & Worth Valley Railway says the heritage award is a nice "accolade to have".
The audience will arrive on the stage by train and a steam engine will take part in the production.
The former triathlete took part in the 50th Oxenhope Straw Race on Sunday.
The road closure will begin on 2 June at Keepers Lodge and a diversion will be in place.
Children aged from eight to 15 are invited to audition for a production of the classic in Bradford.
Footpath along the River Worth has suffered from vandalism but is now more accessible.
