This question involves two separate episodes, so I will try to address both of them.
In Boris Pasternak's novel, the principal confrontation between Zhivago and Strelnikov (whose real name is Pavel Antipov) occurs near the end of the story. In the eastern region where Zhivago and Lara had been together, Strelnikov improbably meets with Zhivago and does not so much debate him as philosophize with him on both political and personal issues. In spite of their differences, a bonding of sorts occurs between them. It is an ironic episode between the two because, in some sense, they have represented opposite sides of the huge conflict of the Revolution. They have also both loved Lara. Zhivago is a poet, a dreamer. Strelnikov is an idealist of sorts as well, but his whole plan has been to serve the Bolshevik cause, apart from Lara, for as long as he is required in his political task, and then somehow to go back to her, become Pavel again, and restart the old life where they had left off. It hasn't worked out that way. After their meeting is over, Zhivago finds Pavel outside lying in the snow, dead, having shot himself.
In David Lean's film version of Doctor Zhivago it is much earlier in the story that Zhivago, on his train route east with his family, is detained and questioned by Strelnikov, who tells him harshly that "the personal life in Russia is dead." Strelnikov makes it clear that the end justifies the means in completing the task of the Revolution. Zhivago does not seem to question the supposed goals of the Bolsheviks in creating an equal society for all, but he stands up to Strelnikov in condemning their brutal methods. Strelnikov has suspected that Zhivago is a "White" (anti-communist) agent, but he nevertheless releases him and allows him to rejoin his family.
In both the novel and the film, Zhivago and Strelnikov/Pavel represent opposites: the one a poet-dreamer, the other a man of action—not without ideals, but using harshly practical methods. Yet both seem motivated by a desire to transcend the pre-Revolutionary Russian world and to accomplish something positive for humanity, each in his own way. That Pasternak has both of them in love with Lara is perhaps symbolic of this commonality.