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It's not clear which scientists you're talking about. I can answer you about mathematicians and physicists.
In mathematics, it is difficult to shake any theory; you can test the theory experimentally, the more experiments, the more reliable it is, but this is not strictly, so rather for confidence, like the 4-color theory: it was not proved, but the computer seemed to always be able to color the graph properly.
The only thing that can shake mathematics is the inconsistency of set theory or arithmetic, although this is unlikely to greatly spoil the results used in practice: group theory, numerical methods, probability theory, etc.
In physics, everything is simpler. Classical mechanics is not questioned, and neither are thermodynamics and electricity. The theory of relativity is difficult to refute, as well as string theory, because you need expensive experiments for this, and no one will give you money for them.
1) If we understand the question as follows: Will a scientist be deprived of degrees and titles if his theories turn out to be untenable? The answer is: “No, they won't.” The mechanism of deprivation is very cumbersome. It is usually applied if there is evidence that the degree or title was obtained illegally. The resulting “crusts” are not taken away for scientific errors, even if incorrect theories have caused harm to the country. An example is Academician T. D. Lysenko. 2) If you understand the question like this: Does the applicant fear that they will not get the degree or title they are looking for if the generally accepted theory is shaken? Answer: “Yes, he is afraid.” And in the politicized humanities, he is very afraid. How many finished dissertations were lost when N. S. Khrushchev was unexpectedly removed, or when L. I. Brezhnev died!
By “currently accepted theory” do you mean current scientific concepts or proven theories? Awards and titles are given for very real rigorous research and evidence. And scientific ideas-quite a “wobble” and change.
Let's look at the history — phlogiston, caloric, light-bearing ether. These were all scientific hypotheses and were not proven, just the opposite, research in these areas led scientists to other conclusions. Many famous scientists were adherents of such hypotheses, which did not “shake” their scientific achievements in any way, even if they started from incorrect ideas. No one doubts the merits of Newton, Huygens, Ampere and others.
It is very difficult to shake a proven theory, since the requirements for proof are very strict and are checked more than once. Anyone has the right to check and criticize (only in this case they will have to work hard, because they themselves can get into a puddle because of unfounded criticism). The well-known theories that are now being taught have been criticized by the scientific community for a very long time.
Over time, theories are updated, corrected, and refined. The new theory should not only explain where the old theory is wrong, but also why it worked. So it turns out that almost always a new theory is a reinterpretation of the old one and explains its conclusions, adding new facts and evidence.
So, if tomorrow you hear that General Relativity has been “refuted”, then either it is a new, more general theory that looks at the consequences from a slightly different angle and essentially includes it, combining it with other theories (the entire scientific community is waiting for this event). Or another piece of nonsense that has nothing to do with science.
I hope I got the message across. Scientists are more afraid to make a loud erroneous statement, so they take a very long time and carefully double-check their conclusions. It happens.
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“…can such a factor (“Oh no! They have discovered something that is not profitable for us!”) be a reason for “silencing” some amazing alternative theories :))”
The scientific community is a competitive environment and not very “friendly” – scientists from different countries who pursue different goals and share different ideas will not be able to” agree ” for the benefit of one group. And in the imaginary case that someone actually makes a groundbreaking discovery that will lead to a revision of some concepts, this competition will force scientists to race in new research based on the new discovery. It seeks to leave its mark in the light of the opportunities that have opened up, and not to keep silent. Yes, at least because for this case you can have fun “mastering the budget”.