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XOOPS itself does not rely on allow_url_fopen, but some third-party modules do; just like some require register_globals to be on. This, of course, is shut off as well with many hosting providers.
The only time I've found turning allow_url_fopen to off a problem has been with custom blocks for some advertisements or displaying content from a page hosted on another server. The easy workaround for this is the use of iframes.
As far as core functionality with XOOPS or any of the higher quality modules, turning allow_url_fopen and register_globals to off presents no problems whatsoever.