Yes, as you say, science is always changing. However, it might be better to say that science is always advancing. That does not mean that the foundations of science are unreliable. Scientists now know a lot more about the shape of the Earth than Aristotle did, but that doesn't change the fact that the Earth is very nearly spherical. Scientists now know a lot more about the movements of the planets than Kepler, Galileo, Newton or Laplace did, but that doesn't change the fact that the planets, including the Earth, revolve around the Sun in elliptical orbits.
You are comparing apples with mushrooms. The theory of evolution by descent with modification from a common ancestor is a scientific hypothesis; there are many ways of testing it (e.g. genetics, comparative anatomy, and palaeontology), and, so far, it has passed every test. Of course, like all scientific theories, the theory of common descent will be modified by new data and new research, but, so far as I can see, it is no more likely to be completely disproved than are the heliocentric theory of the solar system or the thermodynamic theory of heat.
(By the way, you appear to be moving the goalposts here. Originally you said that science is unreliable because scientific theories change, but now you are saying that scientists won't recognise common design 'because common ancestry is the rule of thought'. Your argument would be more consistent if you said that theories of common ancestry are unreliable because scientists once thought that birds and insects are descended from common ancestors or that walruses and octopuses are descended from common ancestors.)
The 'theory' of common design, on the other hand, is based on assertions about the actions of a supernatural being. It is not a scientific hypothesis; there is no possible way of testing it, and a defender of common design can reply to any objection by saying that God chose to do it that way and His (or Her) ways are inscrutable.
That is why the debate between evolution and the various forms of creationism is so intractable. A scientific debate will eventually be settled by an accumulation of evidence in favour of one hypothesis or the other. However, the opponents of evolution are not basing their arguments on scientific evidence but on a conviction that a particular interpretation of the Bible is correct; such a conviction can never be overturned by evidence to the contrary. It's like the story of the two fishwives screaming abuse at each other from the top-floor windows of houses on opposite sides of the street; they could never agree because they were arguing from different premises.