French Marxist Louis Althusser argued in his paper Ideology and Ideological State Apparatuses that there is no beyond or outside within which we can exist. Instead, we are always already interpellated, called into existence.
Thus ideology hails or interpellates individuals as subjects. As ideology is eternal, I must now suppress the temporal form in which I have presented the functioning of ideology, and say: ideology has always-already interpellated individuals as subjects, which amounts to making it clear that individuals are always-already interpellated by ideology as subjects, which necessarily leads us to one last proposition: individuals are always-already subjects. Hence individuals are ‘abstract’ with respect to the subjects which they always already are. This proposition might seem paradoxical. (Source)
Adding to this, Althusser highlights that there is no point outside of ideology:
What thus seems to take place outside ideology (to be precise, in the street), in reality takes place in ideology. What really takes place in ideology seems therefore to take place outside it. That is why those who are in ideology believe themselves by definition outside ideology: one of the effects of ideology is the practical denial of the ideological character of ideology by ideology: ideology never says, "I am ideological." Source
Coming from a different perspective, Michael Foucault discusses the challenges of identity in Archaeology of Knowledge where he states:
Do not ask who I am and do not ask me to remain the same: leave it to our bureaucrats and our police to see that our papers are in order. At least spare us their morality when we write.