So, before I begin, I want to bring back in some context that is important to the point I want to make. Alito made his statement in response to a juror fighting summary rejection from a case, in which the rejection was due to their belief that "homosexuality is a sin." The plaintiff, in this case, identified as a lesbian.
I think it is very important to point out that Alito is being very careful in picking his focus of concern from a constitutional perspective as, you have to remember, the sixth amendment garuntees "speedy and public trial, by an impartial jury". To put it another way, the court try to eliminate, from they jury, pool any individuals whose bias would negatively affect the outcome of a case in a way not congruent with the law. To me, it seems very intentional that he would champion one constitutional right and neglect another as Alito, a Supreme Court Justice, should be taking all angles of the constitution into question. He should not take into account just those parts that align with his held bias and beliefs.
Now, how should we as individuals, considering both the 1st and 6th ammendments, broach asituation in which two individuals right clash?
I have tried to look into if there was any precedent on determining what happens in the case of conflicting constitution rights, but I could not find anything. So, as to my limited knowledge, I can't really look to precedent (if someone knows anything about this, please share).
Personally, I would believe that since it could be the matter of someone's freedom on the line in the case of a trial, I lean in favor of the summary dismissal. Not being on a jury does not, in any way, amount to an injury to said individual that in anyway compares to the possible ramifications of allowing bias onto a case in which someone's life or property is on the line. The individual can continue to believe whatever regressive asinine dogma their religion subscribes to(and yes, I am showing my bias), while the case is decided by people more willing to only consider the law of this country and not some diety who has no authority here.