Profaci was the don. Neil was supposedly helping the don. Not sure how that could be against mob protocol.
Now, if Neil was sponsoring the insurgents, then I could see how that would ruffle feathers.
Neil wasn't the don of his family however. If Carlo wanted to publicly remain neutral, then Neil would be in trouble for helping out either side. Profaci would have to ask Gambino to get Dellacroce's help. So Dellacroce was either usurping Carlo or going behind his back by helping out Profaci, neither of which would be good for him.