The planet is called opinion which allows others to have them as this is a forum ? be they right or wrong I would not personally base my entire business plain around them, but take parts onboard and discard other.
As most clubs as you say yourself “clubs don't like having their name associated with anything where they don't make money.” Then the likely hood of them granting you permission without financial gain and stringent rules as to what you can put on there making it hard for you to monetise the site is pretty slim
Busking and domain names?
As the poster says there are two other clubs with the same initials then Newcastle United and Nottingham Forest. As they have different initials it could not be both of them?
There are other clubs with the same initials just because you set up a site for one does not mean the others would not make claim to the domain name and your affiliation to one could have a bearing should the others have a higher claim and your cast iron defence would not be very good to the name (ignorance of the laws governing trademarks etc is not a valid excuse under British law but could be used as mitigating circumstances), normally only one would be judged to have a claim to a name ?
If you had gunners.co.uk as a fan site for Chelsea do you not think arsenal would not object?
In an ideal world yes get approved but in a business world very unlikely
as you have said you should change your name to Red Kite in posts are you sure you have not