The difference is that there exists a sound explanation for that apparent disagreement, one that can (in principle) be understood by the flat-earther. Are you suggesting a scenario in which a sound YEC explanation would somehow "fall from the sky" for the entire body of evidence in every field of science relevant to this question? In that case, I might be able to continue doing my research but then within that new framework (after serious reschooling!). Though it would look nothing like any YEC researcher has come up with so far. In that case, I would actually be very curious to find out what it would look like!
I have tried to explain that my research is largely about understanding the evidence of past events. In your hypothetical scenario, that evidence would become meaningless and the corresponding past events would be non-existent. Therefore, I would have nothing to do research on. It is an answer to your question in practical terms.
It is different in astronomy, because we are mostly observing events that happened thousands, millions, and billions of years ago (because of the time light needs to travel towards us). We are always looking at the past. 99,9999% of the observable universe lies beyond the distance that light can travel in 10,000 years. In most cases, we are directly observing the universe as it used to be, millions of years ago. In that sense, astronomers are living in the distant past, most of the time .
It saddens me that I have given you the impression of being unwilling to consider your hypothetical, because it was my sincere intention to do so. I actually enjoyed letting my imagination run loose. It made me realize that, in that hypothetical scenario, my area of expertise would simply cease to exist. I have seriously considered your hypothetical and this is an honest answer.
If there would be a completely new form of expertise that could replace my work (as described in the first paragraph of this post), I would probably learn about that new framework and start working within that. But that would still involve a huge change of career. This cannot be framed any other way, I'm afraid.