All Jews are Mamzerim III

Another consequence of all Jews being statistically mamzerim is that, despite what The Temple Institute says, it is forbidden to renew sacrificial worship. If all Jews are statistically mamzerim, it follows that all male descendants of Aaron  are statistically halalim, and so are not kohanim. Sacrificial worship requires the participation of kohanim. For example, the sacrifice of an animal includes at least four steps: slaughtering the animal, collecting some of its blood, carrying the blood to the altar, and offering the blood on the altar. Only the first step may be performed by a non-kohen.

A halal (חלל) is the son of a kohen and a woman whom he is forbidden to marry. Those who want to renew sacrificial worship might argue that the son of a kohen who is "just" a halal (for example, a son of a kohen and a divorcee) may participate in sacrificial worship. As RaMBaM states (הלכות ביאת מקדש ו:י)

כהן שעבד ונבדק ונמצא חלל עבודתו כשירה לשעבר ואינו עובד להבא ואם עבד לא חילל שנאמר ברך י"י חילו ופועל ידיו תרצה אף חולין שבו תרצה

Chabad translation:

When a priest performed service and afterwards, his [genealogy] was checked and it was discovered that he was a challal, his previous service is acceptable, but he may not serve in the future. If, however, he does [continue] to serve, he does not desecrate the service. [This is derived from Deuteronomy 33:11]: "May God bless His legion and find acceptable the work of his hand." [implied is that] He will find acceptable even the desecrated among them.

But this is not the case for a halal who is also a mamzer. The Encyclopedia Talmudit article on halal says that there are differences of opinion among the Rishonim about whether sacrificial worship by a kohen mamzer is valid retroactively; but nobody maintains that a kohen mamzer is allowed to participate a priori in sacrificial worship. RaSHBA (reference 466 there) distinguishes between sons of women who are prohibited only to kohanim (פסולי כהונה), to whom Devarim 33:11 applies, and sons of women who are prohibited to Jews generally (פסולי קהל), to whom Devarim 33:11 does not apply.