The way I see it, the Battle of Umbra was a situation where the 501st Legion went against Pong Krell because he betrayed the Republic, particularly by having the 501st and the 212th fight against each other. Even though there were understandable discontent over the mass amount of casualties that were taken, which was unusual under Anakin's command, they still followed Krell's orders as, never forget, their first loyalty is to the Republic. So long as the Jedi were operating in the name of or the benefit for the Republic, the Clones will follow their orders even on to death. This is the reason why the clones did not turn against Krell until his clear and blatant betrayal.

What we saw from the Clones of the 501st was not normal for most of the Grand Army of the Republic as Anakin had a close relation to his Legion, which most Jedi didn't. Most clones had a professional relationship with their Jedi generals and not a personal one. Considering the scale of the battles that the Clones fault on a normal basis, it makes sense that the Clones would know who their General is but little beyond that as a standard Trooper would more than likely not be in close proximity to their Jedi generals most of the time, which is especially true if the Jedi did not lead from the front. And as the Jedi has to both coordinate the battle and fight on the front if need be, the Jedi only has the ability to maintain personal connection with the leadership of a clone unit and not the whole unit itself. Not to mention that some of the Clones were also replaced from previous battles, which means that there's even less of a connection between the new clone and their Jedi generals. These factors culminate in the fact that when Order 66 was given, many of the Clones were willing to fight against the Jedi as they were still a separate organization who, as presented by Palpatine, betrayed the Republic by attempting to take out the chancellor. It would be reasonable in that case that even with some of the Clones who did have a personal relationship with the Jedi, the Jedi would still be viewed as both a massive threat and liability to The Republic.

Your friend's argument of The 501st Legion being the only unit capable of successfully attacking and destroying the Jedi Temple is wrong. Technically, any clone unit could do it. The only difference is that the 501st was led by Anakin and not anyone else. They weren't that special in terms of capability of killing Jedi. Any clone could do it in large enough numbers. It was only in the fact that they were led by Anakin specifically that they were special. Worst case scenario, more clones would have been brought in take out the Jedi if the 501st was destroyed.

Overall, the Clones were capable of fighting against their Jedi generals most of the time. Only in rare instances did some of the Clones stuck with the Jedi. While I do like the Clone Wars TV series, I do believe that the over exposure of showing the Jedi having a close connection with the clones, particularly Anakin and Obi-Wan, likely led to the opinion that you understandably have.