They just have to get used to the new you, and that requires lots of lots of reinforcement of the new image from you. If you're young, it'll succeed in a couple of years. If you emancipate at 40, like I did, chances of it never being accepted are high, though. The most important is to work on your guilty feelings so you don't relapse out of a sense of guilt.
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So-called white lies are like fake jewelry. Adorn yourself with them if you must, but expect to look cheap to a connoisseur.