Maybe, but it isn’t the same.
There are two ideas that need to be unpacked here: intersectionality and the systemic nature of racism. Racism is a system of oppression built around the idea of white supremacy. Racism is historical and on-going, maintained through legal, societal, and personal actions, laws, and beliefs. Racism is not undone through individual action although it is experienced and propelled at the individual level. Part of the complicatedness presented in statements like these is that, as a white person alongside our multiple identities, we may believe we can be individually excused or held separate from the systemic nature of racism. Simply by existing in a racist society, white people are implicated in the system of racism; therefore, only by actively working against racism (antiracism) might we someday change the system, although typically not in the present moment (see Kynard “Racial Realism”). To make any claim to innocence or exemption from racism (especially, on the basis of having other oppressed identities, such as being a woman, or coming from a lower-income background) can elide the responsibilities of engaging in antiracism as a white ally. There is also a historical precedent of gender, sexuality, and class based critique being deployed as a means towards social reforms that in practice reinforced racial hierarchies in the US.
A lack of privilege in class or gender or sexual orientation or ability is not exculpatory. And while we carry complicated multiple identities that lead to intersectional ways that systems of oppression manifest in our lived realities, no intersectional experience negates whiteness to the point of lack of white privilege.
Part of anti-racism is working to understand the complex, ever-changing nature of oppression: for instance, that one can be privileged as a white person, yet oppressed as a person with a disability, or as a woman. Naming and understanding one’s own positionalities to oppressive systems and ideologies is key. Recognizing one’s own experiences as an oppressed person may even help build empathy and understanding of another’s differing experiences. Though we may never fully walk in another person’s shoes, we can recognize that their walk is specifically difficult, in ways that may be both similar to, but fundamentally differ from, our own. We can also leverage understanding of our own experiences of oppression to create strategic alliances across difference. But this is not to say that varying forms of privilege and oppression are the same or remain the same. Forms of oppression can change through time: for example, one may be born into poverty, yet sometimes benefit from enough educational opportunity to move into another class. Also, some forms of oppression are visibly marked (one cannot change their skin color), where others may be more hidden (as with certain forms of neurodiversity). Even this seeming invisibility can provide its own challenges: for instance, making it harder for a neurodiverse individual to have their disability recognized, and thus to receive the support their condition warrants. This is all to say that the importance of understanding one’s own complex positionality is key.