The correct, yet awkward sounding sentence is:
"They cannot all be like I."
The reason this is correct is because the rest of the sentence would read, "They cannot all be like I can be." or "They cannot all be like I am."
Additional support for this comes from www.Dictionary.com:
A traditional rule governing the case of personal pronouns after forms of the verb to be is that the nominative or subjective form (I; she; he; we; they) must be chosen. Some 400 years ago, owing to the feeling that the postverb position in a sentence is object rather than subject territory, me and other objective pronouns (him; her; us; them) began to replace the subjective forms after be, so that It is I became It is me. Today such constructions—It's me. That's him. It must be them.—are almost universal in speech, the context in which they usually occur. In formal speech or edited writing, the subjective forms are used: It was I who first noticed the problem. My brother was the one who called our attention to the problem, but it wasn't he who solved it. It had been she at the window, not her husband.