Behind the saying “beauty is in the eye of the beholder” is the philosophic theory that beauty is a subjective quality that depends on the judgment (or feelings) of the perceiver. This saying could be modified to apply to determining whether an aesthetic object, such as a black balaclava jumper or shoes, is a blackface object: “blackface is in the eye of the beholder.” The underlying principle would be that whether an object is blackface or not depends on the judgment (or feelings) of the perceiver.

If blackface is in the eye of the beholder, then it is up to the beholder to determine whether an object is blackface or not. This might be a matter of judgment or a matter of feeling, depending on the broader aesthetic theory in play. One problem with applying this principle in general would be that whether an object is blackface or not would be subjective. As such, those who assert that an object is not blackface because they do not see it this way would be just as right (or wrong) as those who take the opposite position. However, there is a way to grant a certain audience a privileged right to judge (or feel).
One obvious way to argue for this view is to draw an analogy to insult. Whether something is an insult or not depends on the target of the alleged insult. If the target does not judge or feel that the alleged insult is an insult, then it is not. If the target judges or feels the alleged insult is an insult, then it is. In the case of objects alleged to be blackface, there is the question of who is analogous to the target of a suspected insult
One easy and obvious approach, one that would presumably be favored by those cast as social justice warriors, is that the potential target of any potential blackface object would be blacks. As such, whether an object is a blackface object or not would be decided by the judgment or feeling of black people (and perhaps also those with adequate levels of woke). One could easily get bogged down in the logistics of group consensus, but there are two easy approaches here. One would be to go with the majority opinion of the group. The other would be to break it down to the individual level so that an object could be blackface for one person but not another. While messy and inexact, this does seem to reflect the messy and inexact reality of such judgments (or feelings). Thus, an object would be blackface if the majority of blacks judged (or felt) it is such an object. Alternatively, it could be done at an individual level: an object would be blackface for an individual if they judged (or felt) it was blackface.
One obvious concern here is that whether an object is blackface or not would be subjective. One might raise the objection that under this definition, anything could be blackface, thus opening everyone up for charges of racism. Alternatively, one could argue that if blackface is subjective, then anyone could simply point this out to avoid accusations of racism.
The solution is a messy one: as with disputes over beauty or insults, there would need to be arguments advanced in favor of the various positions and the better arguments should settle the matter as to which interpretation seems to be the most plausible. Even if blackface is in the eye of the beholder, better and worse cases can be made that the judgment or feeling is a sensible one. That no perfect resolution is possible should be expected.
But some might object, being accused of racism has real-world consequences. A person’s career could be ended and their life ruined—surely this should not be left up to subjective judgments or feelings. While, as a practical matter, this is how things tend to work, philosophy does offer a better approach. Turning back to the analogy of insults, there is the question of whether the person making the alleged insult intended to be insulting or not. This can be investigated by considering their history, character and the context of the situation. Likewise, if a work is judged (or felt) to be a blackface object, there is still the question of the intent of the creator. While one cannot know the true heart and mind of another, the creator’s history and character as well as the context can be assessed to reach a plausible conclusion. As such, a person could create a blackface object without intent and without being a racist, just as a person could horribly insult another without any intention to do so. In such cases, the object should be condemned but the creator should be held innocent of racism. Naturally, if the creator’s history and character and the context provide evidence of racism, then that is another matter.