i think this was a lesson i found myself learning early in life, because i had pretty early awareness of the fact that there were a few people in my life that i was related to, and loved, but really didn't like.
i think this pushed me to seek to understand them more. i found myself studying psychological and behavioral studies, articles and books. i needed to understand how we could all be related and yet, so very different about things that seem so very obvious and easy to me.
though this desire and learning, i found myself trying to see the world through their eyes, if i were them, walking in their shoes, saddled with their limitations, desires and personality. and through that, i found a lot of compassion. i was able to see how in some ways, i was more advantaged than them, and also, to have compassion for their current condition, and the behaviors that i found so painful or difficult.
this kind of methodology works for me for others. when i am repelled by someone, i focus on what it is that i object to, seeking to articulate it for myself. when i do that, usually i find that the reason i have such a huge reaction or inability to "like" them is something about me. either they do something that i either do or used to do (that i dislike in myself) or that they remind me of someone in my past who has caused me grief.
then i set out to really try to understand what their struggle in life is. are they hugely insecure? well, that is a horrible, miserable condition that i would feel bad for anyone who really struggles with that. or whatever that condition or struggle(s) that i can identify, i will then consider what that feels like, either through my own current or past issue with that, or through another source.
it seems like when i've spend a decent amount of effort to really understand their battle and condition, i may not want to spend a lot of time with them, but my heart is softened by this effort to "life and feel" in their shoes.
when this person is someone who has to be (or will be) in my life, i.e. working together, i try to communicate as much as possible. if the reason someone is bothering me is because they do something that i find upsetting, i usually will approach them and share the feedback and make a request that they stop treating me a certain way--if that's applicable. or talk to them with the intention of opening communication and seeking their impressions and forging something that will ease the situation.
while it's pretty rare for me to have real vitriol for someone, if that is the case, the best solution (bar none) for me is to pray for them. pray for my heart to be softened, and to pray for their welfare or whatever their needs are. that seems to work well for me with the "strongly disliked" group too.