The stranger in ancient Israel did not serve as a judge, although he received all the benefits of living in the land
We don't live in ancient Israel, nor do we live in any sort of theocracy.
The political question is this: By what biblical standard is the pagan to be granted the right to bring political sanctions against God's people?
Simple, your "biblical standards" have no bearing on US law. Period. Nowhere in the constitution, the founding document of the country, will you find a reference to any holy book or the "laws" and "standard" found in them. Non believers are afforded the same rights and tasked with the same civic duties as the believers of any faith.
Under US law, being a christian does not impart any special status, exclusive rights, or set you above the non believer, and your assumption that it should flies in the face of everything the US was meant to be.
We recognize that unbelievers are not to vote in Church elections.
There is no statute in US law a forbid non believers from voting in church election because that is a matter between the church and it's congregation, not a matter of civil law.
Why should they be allowed to vote in civil elections in a covenanted Christian nation?
Except the US is not a "christian nation". The founding doucument of the country does not so much as mention christianity, which is something you would think would be of paramount importance to a supposed "christian nation".
What I want to know is why you think that only christian should be allowed to elect the people who govern us all, christian and non-christian alike. What constitutional basis do you have for disenfranchising all non christians, especially when most christian denominations consider all the other sects of christianity to not be "True Christians(TM)".
What you proposed is not the freedom enshrined and enumerated in the constitution, instead you offer a society with a religious oligarchy where a persons rights are contingent upon belonging to a certain religious sect that claims it posesses the right to place itself above those it sees an lesser than they. It is a world of coersive conversions, mass disenfranchisement, and virtual slavery. It cannot in any way, shape, or form be called freedom.
(Please forgive the Godwin, but it is appropiate) The society you have proposed is no different than that of the Nazi's, all you have done is is take the concept of a supposedly "superior" race lording over the so-called lesser peoples and changed it to a supposedly "superior" religion lording over the so-called lesser peoples.
Which judicial standards will they impose?
The legal standards of US law and judicial precedent. That is what judges do, they are there to decide matters of US law, not force compliance to extra legal sectarian religious set of beliefs.
By what other standard than the Bible
The bible is not a legal document, and anything found within is simply irrelavent to matters of both civil and criminal law.
I find it ironic that you belong to a group called "Free" Republic when freedom is antitherical to the position you advocate. It seems that when you speak of freedom you mean "freedom for those who believe exactly how I do and no one else."