By reacting you mean getting easilly tagged by a long range rasengan? You mean his deflecting light ability? Pretty sure Sharingan saw through light in the past. Sure he may block Itachi's line of sight with a rock clone, but what will he accomplish offensive-wise with that? And Magatamas would be enough to destroy the clones anyway. In the long run, it won't pay off
Even if he sees coming, he won't be able to react in time when he couldn't dodge a long range rasengan despite seeing it coming
Actually, Mū's reaction time isn't sluggish at all, not when he evaded KCM Naruto's Rasentarengan at close range from his blind spot [Link 1].
Note that he stopped using jinton in order to dodge. In addition, he also casually dodged Gaara's sand from close range while the other kages got trapped, sensed Ōnoki from above prepping Jinton, and countered with a Jinton of his own
even though Ōnoki had started prepping before he did. [Links 2 and 3]
Mind you, Mū's a skilled sensor, skilled enough to even discern the chakra types of hundreds, if not thousands of shinobi from a fair distance away [Links 4 and 5]. His high level of sensing only serves to augment his reflexes, which go hand in hand with reaction time.
What you used as your example doesn't prove that Mū has bad reactions at all. He simply wasn't expecting Naruto to use his chakra arm to propel Rasentarengan right at him from a short distance away, so he was fully focused on firing Jinton, which he noted to be the faster attack [Link 6].
Mū has to stay stationary while firing Jinton, so he couldn't have dodged in that circumstance because he didn't think he was going to get hit, as I explained.
Anyway, I personally don't believe the sharingan can see through Mū's invisibility. But if you want to argue him getting hit by amaterasu, the intel is full here, so he'll sense the buildup of his technique, see that his eye is bleeding, and proceed to fly away from his sight at a fairly fast pace, considering he should be as fast as Deidara is on his bird [Link 7]. If he gets hit, which is unlikely, he can just split himself and continue fighting. This is not even mentioning the Iwa bunshins which can be used as distractions.
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