We study spectrum sharing between two dense low-earth orbit (LEO) satellite constellations, an incumbent primary system and a secondary system that must respect interference protection constraints on the primary system. In particular, we propose a secondary satellite selection framework and algorithm that maximizes capacity while guaranteeing that the time-average interference and absolute interference inflicted upon each primary ground user never exceeds specified thresholds. We solve this NP-hard constrained, combinatorial satellite selection problem through Lagrangian relaxation to decompose it into simpler problems which can then be solved through subgradient methods. A high-fidelity simulation is developed based on public FCC filings and technical specifications of the Starlink and Kuiper systems. We use this case study to illustrate the effectiveness of our approach and that explicit protection is indeed necessary for healthy coexistence. We further demonstrate that deep learning models can be used to predict the primary satellite system associations, which helps the secondary system avoid inflicting excessive interference and maximize its own capacity.