People run rigorous psychology experiments all the time; it's one of the more-sound experimental fields. The only real constraint is that because it deals with human subjects, there are limitations on what types of experiments can be conducted.
Sociology is harder to run experiments, because it deals with interactions among groups of people, rather than individuals. Nonetheless it benefits from natural experiments taking place all around us all the time. This opens it to a different set of confounds, because you cannot precisely design experiments to control them, but you can still do science. You cannot falsify arbitrary theories, but you can falsify many theories.
Ditto climate science; we can formulate numerical models, and refute them by comparing to the ongoing ground truth around us. We can use those numerical models to examine what would happen with perturbed environmental conditions. This a sound computational science for small perturbations. For larger perturbations or very long timescales, you will not have the necessary stability guarantees, but that doesn't mean that you can't do science.
Much of economics is secretly math. You have theorems and proofs rather than experiments. You're correct that this isn't science, but it's not trying to be, and that's OK. The remaining body of economics includes behavioral economics, which--much like psychology--is absolutely science, and can be done extremely rigorously, and macroeconomics, which is largely in the same boat as sociology; they have to take advantage of retrospective studies, but in a sufficiently diverse set of regional economies, you can do some science--you just can't always control for every confound via experimental design.
