The phrase "jury of his peers" does not actually appear anywhere in the constitution. An "impartial jury" is required.
The 6th Amendment in full:
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.
Case law has determined that jurors cannot be excluded from the jury, or from the jury pool, based on their race, gender, or other such traits. But there is no law, and no case law, anywhere that says that an accused has a right to a jury comprising people with a similar lifestyle to that of the accused.