Will people in Boston take offense if you wore a Los Angeles Dodgers cap in their city?

I plan to visit Boston and parts of Massachusetts/New England in a couple weeks. I'm a California girl from the LA area. I hear that Boston is the only city in the country where you cannot wear any caps representing other sports teams, only Red Sox. Or the locals will angrily harass you.

Is this true? Or should I leave my Dodgers hat at home?

Updates
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And it's not just during game day, but in general. I've heard that in the middle of winter, some visitors had their (insert mlb team/city, sans Boston Red Sox) caps snatched off their heads and burned by Bostonians. Tell me that doesn't happen.
Will people in Boston take offense if you wore a Los Angeles Dodgers cap in their city?
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