Biomimetic membranes that adhere to a solid substrate or another interface via switchable crosslinker molecules are studied theoretically using analytical methods and Monte Carlo simulations. The flexible crosslinkers exhibit two conformations which have a different end-to-end distance and, thus, lead to different local separations of the membrane from the substrate surface. Transitions between the molecular conformations can be induced by light, electric potential, or changes in pH and lead to active shape fluctuations of the membrane and, thus, to an increased membrane roughness. The forward and backward transitions are characterized by two transition rates, omega(+) and omega(-), respectively, which define the average fraction X=omega(+) /(omega(+) + omega(-)) of + (or on) states and the mean switching rate omega = (omega(+) + omega(-)) / 2. The membrane roughness is explicitly calculated as a function of X and omega. It is shown that the interplay of active and thermal fluctuations is subtle and that it is, in general, not possible to describe the active fluctuations in terms of an effective temperature.