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Will using rel="nofollow" avoid the penalty?
This is a new one on me. Can't imagine it's real. Certainly, never experienced it myself and we definitely use varied anchor test to same pages within the site. And, trust me, we have very good rankings.
I wouldn't waste any time on this.
I mean, looking at blogs and stuff. I am sure they link to past posts/pages with different emphasis and therefore different anchor text. And, like I said, so do we even within our online store catalogue.
Be careful about what you read and taking it too much to heart. You may not have understood the complete situation - maybe even the person writing didn't understand it fully.
The same menu item in the same place in an identical menu tree (sya in the top bar) should probably have consistent anchor text. But, another adhoc link or even a regular link in an alternative menu (like the sidebar) can be different.
Never had a problem with that.