You have asked which of the following is preferable:
It's really unfortunate that most people cling to something that is not themselves just to get what they want.
It's really unfortunate that most people cling to something that is not them just to get what they want.
I am going to slice away some otherwise-debatable portions of the above as not relevant to which is preferable, leaving the following for discussion:
People cling to something that is not themselves.
People cling to something that is not them.
I think the latter is preferable, as it evokes the well-known phrase “But that's not me”. Of course both are slightly clumsy, and I think the following should be preferred:
People cling to something they are not.
Regarding some of the sentence's other issues, (1) I see no problem with the word cling, although some comments have discussed it lengthily and as if it's a problem, and (2) I question the sense of the statement, as such clinging, fronting, or masking may more often be done not “to get what they want” but to fit in or to avoid peer pressure.