In short: yes.
Longer form:
Algorithms 'discriminate' (as in differentiate) because that is exactly the job they are tasked with. Is this a picture of a person on list A or not? Is this a picture of criminal activity X? They discriminate on a large number of, often hidden, unknown or not understood features in the data.
In many countries the laws dictate that some features such as race, religion, sexual orientation, ... are protected, as in not legally allowed to be used in differentiation. (Take note that in many countries certain national security/safety related organizations are exempt from certain regulations).
The models that are used in facial recognition rely (in part) on 'sub-symbolic' probabilistic feedback systems, that in many cases defy post rationalization: we do not have a convincing or specific 'story' about how 'the machine' decides in each cases. This means we can not deductively prove that the above mentioned 'illegal' forms of discrimination were not used (note that it is not sufficient to show that e.g. 'race' or 'gender' was not explicitly used as a feature in the input, as it could be strongly correlated with other inputs or derivations thereof (e.g. type of shampoo bought, zip-code, food preference, ...)
So we rely on things like testing post training deployed model to 'vet' the systems aren't biased in the ways we by law and regulation have deemed that they should not be. We test whether the output distribution shifts when we only feed in males vs a mixed gender test set etc.
In practice this means that in compliance testing we replace deductive reasoning with correlation. We accept that this will yield false positives, but this choice is partly due to technical limitations (apart from a few well published cases, understanding and explaining how e.g. a deep learning derived model actually 'works' in a rational synoptic way is still beyond us), and part due to ideological stances we have come to.
So, yes, we choose to accept false positives that are presented as evenly distributed across specific protected groups or features, while not 'making a fuzz' over others. These are inherently cultural, political, moral and empathic decisions, not 'logical' ones.