You're misunderstanding the entire situation.
They are not doing this to keep Buehrle "fresh" for the playoffs. They are giving his spot to Stroman because they don't have confidence in Buehrle.
The very first thing out of Buehrle's mouth after the last game is that he felt fine, and he didn't need the 7 days rest. He said he was ready to go 2 games before that. In other words, he was sending a direct message to management that he feels fine, so don't use that an excuse to bench him for Stroman - which they ultimately did anyway. This is absolutely a slight to Buehrle... and who knows what it might lead to in terms of playoff rotation implications.
Why might it piss off some guys in the locker room? For the same reason that you would be pissed off if your best friend on the team, who's been playing with you all year, who you've bonded with, who helped get you to where you currently are, suddenly gets benched for a hyped up young prospect. It's not hard to understand from an emotional standpoint.
A lot of people simply live by the philosophy that you "dance with the person who brought you". I tend to agree with that philosophy in most areas of life, but when it comes to professional sports and especially do-or-die situations like this, in my opinion you've gotta make the decision that gives the team the best chance to win, even if it's at the expense of doing what's "right".
A few weeks ago it may have sounded crazy, but if Stroman lights it up, and Estrada continues his amazing play, then Buehrle could conceivably end up as the 5th guy on that rotation.