My Inatl's policy is that transfers cannot even be considered for affiliation until they have been on campus at least a semester so the Chapter can see grades. There is paperwork that needs to be completed by the Chapter of Initiation and sent to the new Chapter. It also requires a Chapter vote in favor of issuing an invitation to affiliate.
However as KSUViolet said, some Chapters have set a policy of not accepting any transfers. So do your research ahead of time, both about your I/natl policies and where you wish to transfer to.
As for the campus rivalry, in theory that shouldn't be held against anyone. An XYZ is an XYZ regardless of where she goes/went to school. Football, basketball, etc rivalries should be left on the field or court. In reality who knows? But you should be prepared to answer questions about why you transferred. Hopefully it's something like the previous campus didn't have the major you wanted, or the new one has a better rep in your major, or even you don't want to pay out of state tuition anymore. Following a boyfriend or getting away from an ex (unless he's psycho) won't impress anyone.
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