Complex sentence: The Soviet military, specifically the Strategic Missile Forces, was reluctant to support what was essentially a politically-motivated project with little military utility, but both Korolyov and Chelomei pushed for a lunar mission.
Split into simpler sentences: The Soviet military, specifically the Strategic Missile Forces, was reluctant to support what was essentially a politically-motivated project with little military utility. However, both Korolyov and Chelomei pushed for a lunar mission.