Well, then the low charisma of your pc is probably the problem: try making Jaheira (rep. 15) your party leader (drag & drop her portrait in the side column to the top) and then having her initiate the dialogue with Minsc. It might be best going back to a save before the first attempt to initiate dialogue with Minsc, as it is possible that the game engine otherwise will "remember" your previous failed attempts and that Minsc will keep turning you down. But I am not certain about that, so if going back to an earlier save was a major inconvenience you might as well try it first just with a change of party leaders.
Note 1: the charisma for your party leader is very important: a) for the reactions of npcs outside your party to your party when interacting (see above)
b) for the battle morale within your party: if your party leader has got a high charisma your party members are less likely to panic when a battle turns out to be very taxing.
Note 2: your notion that you want to win the respect of your party members through your deeds rather than through your stats is one I can really sympathize with, but I am afraid it is also one that is asking way too much of the game engine/ A.I. ! Remember computers are mere number-crunchers, their "social intelligence" is zero ....
Good luck and have fun !
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So long !
R³ - proud to be the official spokesman for the most noble Lady Bilqis, Desert Rose of Ironworks
Btw, the cow is queuing in the slaughterhouse right now !