I am having the exact same problem on my iPhone 4S after installing iOS7
Today I installed iOS7 and since the upgrade the wifi is now greyed out and I can not get it switched on anymore.
Tried several restarts, have reset the network settings but all to no avail.
However Bluetooth still does work, but the BT sound quality has drastically deteriorated since the upgrade to iOS7 to the extent that people can no longer understand me, making BT no longer usuable.
(until this morning the use of Bluetooth was flawless and crystal clear using my Plantronics Voyager headset)
So far in this discussion I see no response from Apple in this issue.
So it seems we are all out in the dark on possible solutions which only Apple can provide.
My iPhone is now a little over a year old and I find it hard to accept that Apple would not assist her customers in solving a problem caused as a result of the iOS7 upgrade.
Furthermore I NEED my wifi when travelling abroad and I fly to Asia next week. Without a working iPhone with wifi I can not communicate with my office.
So if Apple does not come to the rescue I'll have no choice but to purchase a new phone. And I can assure you, in that case it will mostlikely not be an iPhone.
Therefor my plea here on this Apple website to the Apple support team:
Please come to our rescue and assist your customers in finding a solution to this problem!!