SAN FRANCISCO — Gay rights groups’ attempt to intervene in a federal challenge of Proposition 8 has created a rift with the high-powered attorneys heading the case, turning erstwhile allies into head-butting competitors.

Both sides have diverging visions of legal strategy. The gay groups are pushing a cautious, narrow approach based on the circumstances of Prop 8, while Theodore Olson, David Boies and their backers are seeking a decisive victory for all gay couples under the U.S. Constitution.