Their motivations varied and often intertwined; but, whether it was due to a desire for glory, wealth and power, knowledge, or religious converts, the entire worldview of Europe and Asia radically shifted after these expeditions.
First, semicolons come between two interdependent clauses.
Second, “but” is a coordinating conjunction. Coordinating conjunctions introduce coordinate clauses. Coordinate clauses are joined to the preceding main clause by a comma if they coordinate closely with it. Or if not, a period is used.
Third, you don’t provide enough context to give anyone any idea how closely related those clauses are because we don’t know whom the possessive pronoun “their” refers to or how or if whomever “their” refers to is related to the entire worldview of Europe and Asia radically shifting after “these expeditions,” whatever that’s supposed to mean.
In answer to your question, I’m not going to say the subjects necessarily have to be the same because I can’t imagine every situation, nor can I even imagine your situation as it is so vague. I will, however, say that if you were to make them interdependent clauses, the “however” or other contrasting adverbial sentence connector you used would need to introduce a clause that somehow specifically contrasts or contradicts what the subject-verb in the preceding clause conveys in order to create the interdependence that is required to use a semicolon between two clauses properly.