Strategic consultants attempt to find what [will] change in their customers' industries.
I would like to know if I must use will / may / might / could / etc., and why.
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The modals “may,” “can,” and “will” (as well as the conditional or past forms of “might,” “could,” and “would”) are not interchangeable.
“May” is best used to indicate permission or uncertainty.
I am not sure whether I may travel to Ohio. I must check with my parole officer.
Presumably the speaker has the physical capacity to travel to Ohio but does not know whether the terms of parole legally permit such a trip.
I may go to the party if I am feeling better.
In the example above, “may” indicates uncertainty about the future rather than uncertainty about permissibility.
“Can” is best used to indicate capacity.
I can fix that computer
indicates that the speaker has the skills and tools to do the act, but does not imply authority or intention to do so. Consequently, it can also be used to indicate uncertainty of occurrence, particularly in the past form.
I could come on Saturday
indicates possibility without indicating commitment or degree of likelihood whereas
I might come on Saturday
also indicates possibility but implies a relatively low degree of likelihood.
“Will” indicates virtual certainty or intention.
Of course I will visit you, just as soon as I can
The sun will come up tomorrow
does not imply anything about intent, but indicates certainty whereas
It may rain tomorrow
The distinction follows directly from the meanings of those modals. The consultants are trying to find something. If that something will change (i.e., it is fairly certain), then it is "what will change in their customers' industries". If that something might not change, then it is "what may / might / could change in their customers' industries".
You raised the issue of "how it [will] change". The manner of change is irrelevant to which modal verb is used.
You also discussed the fact that the consultants "try to find". However, that verb catena (which is in the main clause) is irrelevant for the meaning of the modal verb in the other catena (which is in the subordinate clause).
Note that there may be some ambiguity about whether the meaning of the modal verb should accord with the writer's opinion or the consultants' opinion. For example, if the consultants believe that something "might" change but the writer believes that it definitely won't, then the following would provide extra clarity for the reader:
Strategic consultants try to find what they believe might change in their customers' industries.