Okay, the Earth isn't actually tilting differently. It's been tilted at about 23 degrees for as long as we can accurately figure. What's actually happening is called precession. The angle the Earth is tilted at relative to the plane of the solar system isn't changing, the direction the tilt is pointed is changing. Kind of like a wobbling top. Except without the falling over part.
Anyway, this doesn't really change anything about astrology, since the astrological signs have never, ever matched the actual constellations. For one thing, it's pretty obvious to even a casual stargazer that the zodiac constellations aren't all the same size. So why do the traditional zodiac signs all have the same length? Because it looks neater on paper and nobody who knew what they were talking about actually ever believed any of this garbage had anything to do with stars, that's why. Sorry, but that's the truth.