Alito and Thomas dissent is basically: the word "sex" does not include sexual orientation. So its not covered by the original Title VII. So if they want protection, they need a new law.
There is a strong legal argument to be made here. If one can simply identify as trans but the law doesn't provide a definition under which this would work, you're opening up ambiguity as to what the law even is and how it's to be used to protect someone claiming such an identification. This is a great case where a dissenting opinion is done for the protection of those seeking title as a protected class from those who will shoot the ambiguity loophole to deny the protection this decision purports to offer.
Except that the majority opinion doesn't rely on someone identifying as trans, only acting in a way not socially in accordance with their biological sex.
They also cite that Congress has attempted to amend the law several times (to date unsuccessfully), indicating that they recognize that the law as written does not cover the classes of sexual orientation or gender identity.
That is probably the best dissenting argument.
And the majority opinion is basically: if you fire a male employee for being with another man, its not a sexual orientation issue since the basis for your firing is that the employee is male. Thus, all protections apply