29 CFR 1601.34 states "These rules and regulations shall be liberally construed to effectuate the purpose and provisions of title VII, the ADA, and GINA" (by contrast 29 CFR 1606.4 says "The exception stated in section 703(e) of title VII, that national origin may be a bona fide occupational qualification, shall be strictly construed". A "liberal construal" of the rules would include as many instances as one could interpret as being prohibited, given the purpose of the underlying legislation. The purpose of title VII is to prevent people from using certain considerations as a basis for employment, so a liberal construal of the act would extend to "because of a belief that X is the case", as well as "because of the fact that X is the case". In addition, 29 CFR 1607.3 says
The use of any selection procedure which has an adverse impact on the
hiring, promotion, or other employment or membership opportunities of
members of any race, sex, or ethnic group will be considered to be
discriminatory and inconsistent with these guidelines, unless the
procedure has been validated in accordance with these guidelines, or
the provisions of section 6 below are satisfied.
Firing on the basis of belief that a set of individuals has a protected characteristic obviously has an adverse impact on the protected class, and is accordingly prohibited, even when one or more individuals is not in the protected class.
Switching to state law, in Cowher v. Carson & Roberts the relevant question is whether there had been religious discrimination against plaintiff, who was not Jewish. The decision rests in part on the finding Lehmann v. Toys 'R' Us, 132 N.J. 587 that "it is the harassing conduct that must be severe or pervasive, not its effect on the plaintiff or on the work environment" – this basically isolates the particulars of the discriminee from the actions of the discriminator. In Cowher, the lower court held that "plaintiff could not meet the first prong of the Lehmann test because he was not Jewish, and that the allegation that he was perceived to be Jewish was insufficient". The higher court disagreed. Drawing on case law pertaining to handicaps as a basis of discrimination, the court stated
Distinguishing between actual handicaps and perceived handicaps makes
no sense. For example, in the case of racial and religious
discrimination, the Law Against Discrimination cannot reasonably be
read to prohibit a landlord from refusing to rent to a member of a
racial or religious minority, but to allow a landlord to refuse to
rent to a person who is only perceived by the landlord to be such a
member.
The general principle identified by the court is that
there is no reasoned basis to hold that the LAD protects those who are
perceived to be members of one class of persons enumerated by the Act
and does not protect those who are perceived to be members of a
different class, as to which the LAD offers its protections in equal
measure