Not only were they not mutually exclusive, but the Centuriate Assembly and Tribal Assembly had precisely the same members (all adult male Roman citizens), just organized into groups differently (the 35 tribes vs the 193 centuries, to give their eventual counts), with one vote to each tribe or to each century. These included both patricians and plebeians, so the Plebeian Council was a subset.
The Curiate Assembly fell into disuse early and featured yet another way of assembling citizens. In this assembly, all citizens could attend, but only patricians could vote, and each of the 30 patrician families (curiae) got one vote.
There's a cute story that makes it clear that the Centuriate and Tribal Assemblies were all the same people. On 31 December 45 BC (incidentally the first 31 December in history since in previous years December had had only 29 days), while the people were on the Campus Martius organized by tribes to elect the quaestors for 44 BC (the consuls for 44 BC had been elected by the Centuriate Assembly some time previously...usually it would have been during the preceding summer, but 45 BC was not a usual year, so I don't know exactly when), word came that one of the consuls, Quintus Fabius Maximus, whose term would have ended that night, had died. Seeing the opportunity to reward a loyal follower, Julius Caesar had the people reassemble into centuries to elect Gaius Caninius Rebilus as suffect consul to serve out Fabius's term. Cicero comments "... in the consulship of Caninius no one breakfasted. However, while he was consul there was no harm done, for he was so astonishingly vigilant that throughout his consulship he never once closed his eyes".