Recent experiments suggest that membranes of living cells are tuned close to a miscibility critical point in the two-dimensional Ising universality class. We propose that one role for this proximity to criticality in live cells is to provide a conduit for relatively long-range critical Casimir forces. Using techniques from conformal field theory we calculate potentials of mean force between membrane bound inclusions mediated by their local interactions with the composition order parameter. We verify these calculations using Monte Carlo simulations where we also compare critical and off-critical results. Our findings suggest that membrane bound proteins experience weak yet long-range forces mediated by critical composition fluctuations in the plasma membranes of living cells. © 2012 American Physical Society.