"blurring of identities" is a correct and usable phrase in written English.
It is typically used to describe a situation in which traditional distinctions between different groups of people or different kinds of things become less clearly defined. For example, "The blurring of identities between nations and cultures has led to increased levels of global interconnectedness."
(There has been some online chatter about Letissier's cultural appropriation, but her collaboration with her dancers feels more like an earnest blurring of identities than a cynical exploitation).
The blurring of identities and organizations meant that it was impossible for the prisoners, or, significantly, the military policemen on duty, to know who was doing what to whom, and who had the authority to give orders.
Here are the battling, estranged brothers and their bullying, alcoholic father; the Western setting (Henry's house is in New Mexico); the haunted past; the confusion between history and myth; the blurring of identities within a family (by the end of the play Earl and Ray seem to have swapped personalities).
"It was frightening," writes David Wallace (a character who shares his name not only with the author but also with another David Wallace at the I.R.S., causing yet further blurring of identities and voices), "like watching an enormous machine come to consciousness and start trying to think and feel like a real human".
There was tension around the merger, as students and educators worried about eroding standards and a blurring of identity.
As the characters' physical perceptions melt into one another, Shaw pulls out the stops to show us what that blurring of identity could mean.
Bratton, the actor/person, is now synonymous with the character, but he welcomes this blurring of identity.
We now live in a pop age where Bowie's blurring of sexual identity resonates with the young more than the Beatles' cultural legacy.
The most fundamental one is that such embryos possess the potential to develop into organisms containing human-derived tissue, which may lead to a blurring of the identity of the human species.
Still, some officials said that a merger of services had the potential to blur issues of identity and image that can transcend cost savings, particularly in a county where neighboring municipalities take pride in their distinctive attributes.
