If everyone was was in the same financial ballpark, then your idea would be valid, but when the top 1% have more money than the bottom 95% there is no chance of equal voice. Gays and transsexuals have been out voted forever since they are outnumbered and out spent by the vast Christian majority.
First you are mixing two points; the first point that rich people have a larger voiced than groups and the second that one group has a smaller voice than another group.
To answer you first point try to name on rich person who has a larger role lobbying his congressmen than any mainstream group such as the gay lobby or the ACLU or the unions, etc. The little people when they belong to those groups do indeed have a larger voice than the rich person.
the second point that one group, say the Christians, have a larger voice than another group, say the Transexuals, is just the way it is with math; there are more of them.
Our country was originally set up with the idea that the powerful majority would not be able to persecute the minorities--but that's long gone and government is for sale to the highest bidder. And YOUR religious group is one of the main causes of this devolution in our country since this is billed as a "Christian" country and you have always had the largest majority.
You are correct that the constitution is supposed to protect ideals over popular notions. The ideal that personal property belongs to the one who earned it is presently a minority opinion that should be protected by the constitution and the popular notions that money should be taken from the rich and redistributed to the poor is the notion that should be abandoned.