I'm gonna be extremely blunt here: you're in college, and you're an adult. Your parents shouldn't be controlling your decision on whether or not you decide to rush. Instead, it should be one where you make the decision and then inform the parents about it.
That said, if after all circumstances considered, you still decide not to rush, it doesn't hurt to go out, be social, find out some info, and make a few friends anyways. If the chapter really wants you, they'll try to get you next semester.
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