The Maximum Entropy principle, principally popularized by Jaynes, is known by most people having studied statistical physics. The way I see it, although Jaynes considered it as crucial in the foundations of equilibrium statistical mechanics and other people in the field still do (like Roger Balian for instance), it is more taught and thought of as a useful way of retrieving the Gibbs' ensembles without thinking too much about what it is we are doing. So, I would say that the MaxEnt is viewed as an interesting and curious tool/phenomenon to which not so much importance is given in practice. Although I am quite partisan of the MaxEnt idea, I reckon it may not be enough on its own to explain the successes and solve the foundational problems of equilibrium statistical thermodynamics. In the recent years, I think the mainstream theoretical physics community has lost a bit of interest in the MaxEnt principle/idea in favour of an allegedly "more objective" way of getting the statistical physics framework based on the theory of large deviations.
As for the validity of statistical mechanics; it is validated in many ways by being able to find out the right constitutive relations between thermodynamics variables in various systems and by relating these thermodynamic observables to microscopic parameters. The whole of the theoretical understanding of gases, liquids and more generally condensed matter physics rely on it. It is fair to say that it is extremely successful. As for comparing actual simulations or theoretical numbers with experiments, there has been huge successes in the calculations of the specific heat of solids for instance. Melting temperatures of crystals are computed on a daily basis with usually very good agreement with experiments and effective interactions (like this one) between mesoscopic particles can only be apprehended with this framework etc... In fact, the list is so long and so broad that I don't know where to really start the list.
That being said, it is worth noting that predictions in statistical mechanics rely of course on the theoretical framework but also equally on the microscopic model used with the theory. A dramatic example is that of the liquid-gas phase transition is atomic and molecular systems. If the chosen range of the attractive potential used between the atoms/molecules is too short, then one never sees the transition as its corresponding critical point is then located below the fluid-solid transition.
Thus, dealing with statistical mechanics is a hard job and testing its predictions is also a very hard job. And when disagreement occur, considering the successes of the framework so far, it is often wiser to look at the model first before reconsidering the theory.