The phrase "change your mind when the evidence changes" is a meaningless at best and harmful at worst heuristic. One shouldn't change their mind whenever confronted with new evidence; one should change their mind (or not) based on the strength of the new evidence.
The heuristic is meaningless if one's previous convictions are so weakly held that they can be swayed by anything. If we take the heuristic literally, then if someone claims that the Law of Gravity is wrong because a balloon floats away from Earth, then the holder of the heuristic would have to agree. That the evidence can be explained better by current theories is irrelevant; the evidence changed, so the mind must change. Thus, the heuristic provides no useful method of analysis and is meaningless.
The heuristic is harmful if one abandons judgement in the service of the heuristic. Related to my point above, judgement is a key advantage of humanity. Our ability to think creatively, analyse and reject, and think abstractly has given us a huge evolutionary advantage. The heuristic, if taken literally, requires the abandonment of judgement. What weight should we give this new evidence? Are there better theories out there? Is there an error in the assumptions? What does past research say? What are relevant data and what are irrelevant? Etc. All of these are judgement calls.
"Change your mind when the evidence changes" is scientism; it's something masquerading as science but is devoid of rationality.