Both sides are right, but the underlying claims are not mutually incompatible. The extent to which wnd is right is very narrow and literalist (in a legally misleading way). EEOC is significantly more right, especially from the legal perspective.
There does exist a political perspective which claims that "the law" is only that which is enacted by Congress (or the legislature), and is not vetoed by the executive. What results is a statute, and the cited article focuses on quoting statutes. However, this is not what "the law" means, at least from a legal perspective. "The law" is not just "the statutes", it also includes the meaning of the statutes as determined by the courts. It is literally correct than no statute enacted by Congress "designates homosexuality and gender confusion as federally protected civil rights". The statute enacted by Congress, as codified in 42 USC 2000e-2(a)(1), says
It shall be an unlawful employment practice for an employer to fail or
refuse to hire or to discharge any individual, or otherwise to
discriminate against any individual with respect to his compensation,
terms, conditions, or privileges of employment, because of such
individual’s race, color, religion, sex
"Protected category" and "right" are terms of art, as a means of concretizing the requirements of the statute. The statute simply says that it shall be unlawful to discriminate against an individual because of his sex (it doesn't even say "her sex").
To actually be applicable, the statute has to be interpreted, and because Congress is not extremely explicit in enumerating all of the forbidden acts, the question has to shift from "what are the words of the statute?" to "what does the statute mean?", or "what specific acts are prohibited?". Making that determination is the job of the courts, and this is where the EEOC is correct.
The courts have held a number of things about what exactly the words of Congress must be interpreted to mean. EEOC gives a list of relevant court decisions which say what the law is (that is, how the words of the statutes must be interpreted). Oncale v. Sundowner Offshore Servs., 523 U.S. 75 is a case where a male was sexually harassed on the job by another male. The court held that "Sex discrimination consisting of same-sex sexual harassment is actionable under Title VII". When Congress enacted this law, they politically "had in mind", specifically, harassment of females by males: but, as the court (opinion by Scalia) said,
statutory prohibitions often go beyond the principal evil to cover
reasonably comparable evils, and it is ultimately the provisions of
our laws rather than the principal concerns of our legislators by
which we are governed. Title VII prohibits "discriminat[ion] ...
because of ... sex" in the "terms" or "conditions" of employment. Our
holding that this includes sexual harassment must extend to sexual
harassment of any kind that meets the statutory requirements.
The court further explains how this law is not a general "civility requirement":
A trier of fact might reasonably find such discrimination, for
example, if a female victim is harassed in such sex-specific and
derogatory terms by another woman as to make it clear that the
harasser is motivated by general hostility to the presence of women in
the workplace. A same-sex harassment plaintiff may also, of course,
offer direct comparative evidence about how the alleged harasser
treated members of both sexes in a mixed-sex workplace. Whatever
evidentiary route the plaintiff chooses to follow, he or she must
always prove that the conduct at issue was not merely tinged with
offensive sexual connotations, but actually constituted
"discrimina[tion] ... because of ... sex."
You can use all sorts of factors for favoring / disfavoring an employee, as long as sex does not factor into that choice. A practice that disfavors an employee who is of sex A and is attracted to members of sex A refers to sex, as does a practice that disfavors an employee who is of sex A and is attracted to members of sex B.
Various cases such as Glenn v. Brumby, 663 F.3d 1312 have affirmed this general idea. In Glenn v. Brumby, the reasoning is a little bit more remote. First, in Price Waterhouse v. Hopkins, 490 U.S. 228 it was held that discrimination based on an employee's failure to conform to sexual stereotypes is forbidden: a woman who "acts macho" is being discriminated against, illegally, when men who "act macho" are not equally disfavored. The Glenn court then says "a person is transgender precisely because of the perception that his or her behavior transgresses gender stereotypes".
SCOTUS has not directly ruled that refusing to hire a person because they have sex with a person of the same sex, or because they have had their anatomy changed in a particular way (or might be so inclined), but the weight of lower court rulings on the matter is such that I find it inconceivable that they would allow sex-orientation discrimination when not allowing other kinds of sex-based discrimination. When the court articulates a particular principle, that principle applies to every analogous instance, until you can find a class of situations that are not analogous and another principle is found that distinguishes the cases. That has not been done w.r.t. same-sex and trans-sexual discrimination.