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Oo gan dit Dana? (Sorry about the spelling, I'm pretty sure that's wrong).
My guess would be that there is no massive overriding magnetic field in a galaxy. Just like a glass of water is made of water molecules, each with a huge magnetic dipole, the glass doesn't affect compasses (neither does the ocean). While the magfields are strong, there are equal(ish) numbers of them in equal(ish) directions to roughly cancel out.
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