You do not have to be able to perform experiments for something to be a science. Do you consider the three subjects above to be science? History? Economics? Archeology? If not, what are they?
I think the inability to perform experiments is one of the main criteria that separates the "hard sciences" from the "soft sciences." Archeology, psychology and linguistics are soft sciences. In my paradigm, history is not a science at all, it's just a type of scholarship like the analysis of poetry. Economics is debatable. For reasons I explain below...
I think it's widely agreed that "science" involves making theories to explain things and then testing those theories with empirical observations. That's what separates science from philosophy or mathematics.
Mathematics is not a science, it is a tool that scientists use (as well as architects and stockbrokers). Mathematics concerns abstractions and pure logic. Mathematical theories can be proven true because it doesn't matter whether the natural universe illustrates them, e.g. Lobachevskian geometry. Scientific theories can only be disproved, they can never be proven true. Every scientific theory comes with the caveat that no matter whether it is true "beyond a reasonable doubt," to use the language of the law, it is never true beyond all possible doubt.
The fundamental principle of science is that the natural universe is a closed system whose behavior can be understood and predicted by using theories derived logically from empirical observation of its past and present behavior. The scientific
method includes the testing of these theories. The scientific method is recursive and the above fundamental principle is subject to testing as well, and in 500 years it has not been disproved.
"Soft sciences" use observation and logical reasoning to derive theories, but they are a little weak on their ability to test those theories. So perhaps the definition of a "soft science" is one on which the entire scientific method cannot be brought to bear.
not all science is about prediction. Look at archeology, most of it is just "this is how things WERE" (or are in the case of current anthropology).
This makes them soft sciences. They use reasoning and observation, but they do not include the entire scientific method.
Comparative religion is just the same, with the inclusion of "this bible story can be traced back to this egyptian story etc" As well as "this bible story was aimed at this group of people because they were like this etc"
Comparative religion can be practiced scientifically, using observation of the natural universe and the logical derivation of theories. I think this would qualify it as a subset of anthropology and/or archeology.