There is a good story behind this.
The offical title of Garryowen is Garryowen FC not Garryowen RFC. The oldest rugby clubs in the country (pre 1890) I think are all called FC rather than RFC. I think some traditional Garryowen members wanted the clubs offical title on the signpost rather than the more common name in usage. I think there is less than 10 rugby clubs in the country who are FC rather than RFC, so it would be a matter of pride to members.
Lansdowne, Clanwilliam, Cork Constitution are just a few off the top of my head, who are also FC.