The field theoretic renormalization group (RG) is applied to a near-equilibrium fluid model associated with a scalar field (like temperature or density of an impurity) that is active, that is, affects the dynamics of the fluid itself. It is shown that the only possible nontrivial infrared asymptotic regimes are governed by “passive” fixed points of the RG equations, where the back reaction is irrelevant. This result resembles the result obtained by Nandy and Bhattacharjee (1998) in a model describing active convection by fully developed turbulence. Furthermore, the existence of “exotic” fixed points with negative and complex effective couplings and transport coefficients that may suggest possible directions for future studies is established.