This question seems to be founded on a mistaken impression of the Culture in the Consider Phlebas era. Interfering in other cultures is something the Culture has always done; that's what Contact Section and especially Special Circumstances are for.
The only desire the Culture could not satisfy from within itself was one common to both the descendants of its original human stock and the machines they had (at however great a remove) brought into being: the urge not to feel useless. The Culture's sole justification for the relatively unworried, hedonistic life its population enjoyed was its good works; the secular evangelism of the Contact Section, not simply finding, cataloguing, investigating and analysing other, less advanced civilisations but - where the circumstances appeared to Contact to justify so doing - actually interfering (overtly or covertly) in the historical processes of those other cultures.
With a sort of apologetic smugness, Contact - and therefore the Culture - could prove statistically that such careful and benign use of 'the technology of compassion' (to use a phrase in vogue at the time) did work, in the sense that the techniques it had developed to influence a civilisation's progress did significantly improve the quality of life of its members, without harming that society as a whole by its very contact with a more advanced culture.
Faced with a religiously inspired society determined to extend its influence over every technologically inferior civilisation in its path regardless of either the initial toll of conquest or the subsequent attrition of occupation, Contact could either disengage and admit defeat - so giving the lie not simply to its own reason for existence but to the only justificatory action which allowed the pampered, self-consciously fortunate people of the Culture to enjoy their lives with a clear conscience - or it could fight
Consider Phlebas, "Reasons: the Culture"