Microorganisms are the most biodiverse life forms on our planet, yet we know little about the spatial processes underlying their ecology and evolution. Here, we highlight the importance of two spatial processes that act on individual cells - spatial intermixing of different populations and mechanical cell shoving during growth - to improve our understanding of microbial eco-evolutionary dynamics. Using an individual-based model, we show that the coexistence of slow- and fast-growing populations becomes highly constrained under two conditions: when the slow- and fast-growing populations are highly spatially intermixed and when the ability to shove other cells (both conspecific and heterospecific) is weak. The potential for evolution through plasmid-mediated horizontal gene transfer between slow- and fast- growing populations also becomes restricted in the same scenario. Our modeling highlights that ecological constraints can dampen evolutionary opportunities within microbial communities due to variation in spatial intermixing and mechanical shoving at the cellular scale.