J'aurais fait tout ce chemin pour que l'on me demande de « changer d'avis » ?!
My guess: = "Don’t tell me I (would) have come all this way, just so ..."
The Past Conditional « J'aurais fait » usually translates into « I would have done », depicting a hypothetical course of action that might have happened in an alternative situation, but obviously in this specific sentence, « J'aurais fait » is used rather differently. I’m not sure how to interpret it.
The implicit beginning of the sentence must be "Si ce que tu me dis est vrai, ...", which introduces a conditional. So it means you can't believe you did it only for this few... Ostensibly, it's disbelief, but often the disbelief is a way to express disagreement.
There is the use of past conditional in French to mean apparently, though not usually in the first person. Here it is.
I apparently came all this way so that I'd be asked to change my opinion?
This use of conditional is sometimes also translated as allegedly in English....but not here. In legal texts or other contexts.
In this particular usage, the translation is not conditional in English. It's simple past plus apparently or allegedly....
Similar to the function of the French conditional mentioned in @Lambie ‘s insightful answer to hedge or qualify the truth of a claim or statement with notions of “apparently,” allegedly” [and “reportedly],” it’s also used
“[s]ometimes [as the] equivalent of English 'might' [or “may”] when the speaker is speculating about possible causes/outcomes [and wishes to imply] greater uncertainty than the future tense [would imply].”
(From French Grammar and Usage by Roger Hawkins & Richard Towell via grammar-now blogspot)
(see also The Conditional Tense from TranslationDirectory,com for an example with the past conditional [“qui seraient intégrés"=“that may be added”] at line 11 and thereabouts)
So with the “might/may” function of the conditional in mind, your sentence could be interpreted as follows:
J'aurais fait tout ce chemin pour que l'on me demande de « changer d'avis » ?!
"[So it’s possible that] I may/might have come all this way [for nothing]"?!
I would translate into
I had to come all this way to have been asked to change my mind?
have to underlines the fact it was a duty (and a pain).
ask on present perfect tense to express the question has been asked but is no longer relevant anymore since changing my mind is out of question and the answer is obviously "no way".
If you want to express even more the annoyance :
I had to come all this way to only have been asked to change my mind?
or
I had to come all this way to just have been asked to change my mind?
