Everyone has to use confirming clubs. But for most of us, the onus is on us to ensure that the clubs we use are conforming (side point: not sure how we actually do that - I guess we do it on trust the the OEMs are making clubs to the conforming specification). But for some elite events, the organisers can use the local rule to restrict driver heads to those that the R&A/USGA have actually tested and approved as conforming. The England Golf hard card demonstrates it - in that any competition they organise which is non-handicap & therefore played off scratch, has the local rule in effect. But any handicap comps they organise are not using the local rule.
Us mere mortals playing in the monthly medal are not covered by the EG hard card, and are not (or shouldn't be) tied to the list of conforming drivers - but we still are required to use drivers that conform. But we have the "luxury" of being able use drivers that conform, but which may not have been tested as conforming.
If a club has been stated as non-conforming by the R&A, then no, you can't use it.