There are those who have common sense, and those who have managed to shed themselves of the burden. There are also those who assume you, the reader, don't have any.
...the general idea that something like relativity is flawed because it contains assumptions
It is said that all arguments rely upon assumptions. I know they all rely upon presuppositions, and I myself doubt that all presuppositions can be obtained as indisputable conclusions.
The problem with assumptions in an argument is pretty simple and obvious: If I don't make the same assumptions you make, your conclusion has no value to me. Yes, folks, I had to say that for the benefit of those who assume you don't have a lick of sense.
This is not the same thing at all as claiming an argument is wrong because it contains an assumption.
Also notice that my statement makes some assumptions compulsory: those which one applies oneself, one must continue to apply when addressing the discussion. One cannot assume the law of gravity when catching a touchdown pass, and then turn right around and deny the law of gravity in order to oppose a premise.
As relating to origins, the problem of evolutionism is that the assumptions made are not compulsory. Most are in direct conflict with at least one observation, but that's another issue. Even when there is no conflict with observation, you have no right to impose any new assumption upon me (as a participant in honest discussion - I'm not talking about law, in case any ninny intends to equivocate).
The great irony is that assumptions in arguments serve as absolute truths, while those whose arguments rely upon smuggling them in, rather than openly disclosing them are always telling us there is no such thing as absolute truth.
Observe the famous loaded question: "Have you stopped beating your wife?"* The assumption is built into the question as an absolute statement of truth.
But this is true of all assumptions. This is the very reason circular reasoning works: once something is assumed, consistent reasoning requires it to always remain absolutely true. Yet circular reasoning is only the most obvious way to abuse assumption. Suppose we're out to prove a given shape is a square, and we lack the actual evidence. If we can introduce the assumptions that it has four sides; that all sides are equal in length; and that all sides intersect at right angles, we have no need of evidence at all. There is no way for anyone accepting those assumptions to honestly avoid concluding the shape is a square.
Assumption might well be defined as "assertion promoted to absolute truth". You will never find a smuggler of assumptions who is willing to divulge them, for obvious reasons.
*It's not actually the perfect trap the prankster thinks it is, either. One who never commences beating one's wife would be unable to cease, any more than you can put aside your plans to destroy the Andromeda Galaxy with your stockpile of leftover fireworks. But such ploys are not for the benefit of the one presenting the question or the one answering; they are meant exclusively to create an impression on other parties.