When I heard about "protecting an identity under the law" from the woke, I first thought they meant identity theft, stealing your passport etc. But no.... they mean something else. What does this phrase mean? Protecting an identity? Like pushing identity politics? Defending that you are whatever race you say you are? Is this about being transracial, transexual, etc? I'm an old school liberal and I just don't get this stuff.
The meaning of words and phrases depend on context. Nobody will say what you quote on it's own, it'll be part of a longer statement which should establish the context. If you still don't understand what that individual means, only they can definitively explain and anyone else can only express a valid opinion with that full context. You'd need to directly quote examples for anyone to make any reasonable comment here.
in my opinion, protecting an identity can come from different view points, like you mentioned.. Identity theft.. and not allowing it to occur with the many 'crooked' ones out there who find doing so nothing to be ashamed about and who find doing so a mockery of sorts... There is also protecting an identity if you are religious in any way.. to protect the 'identity' you have led others believe you to be...
The weird thing is that I see a lot more in common between conservatives and the woke than myself and the woke, yet the woke may indeed call me conservative now.