The first stated duty of the Chaplain of the House of Representatives as a Minister of Outreach is as follows:
"To bring a dimension of faith to human events, giving praise and thanks to God for what God is doing in the world, in the nation, and in and through leaders and ordinary citizens"
While that is not a "endorsement," as you referred to the cross on the LA seal, of any specific religion, it certainly sounds like an endorsement of monotheism. The initial rule, established very early in the history of our current government, was that the House and Senate Chaplains had to be of "different denominations" - clearly implying that a Congress still largely led by men who drafted and signed the Constitution fully anticipated that they should have Congressional Chaplains and that they should be Christian. The use of "In God We Trust" on currency is also an overt endorsement of a monotheistic belief system.
Again, the intent of a Constitutional ban on establishment of religion was always to prevent religious persecution, not to prevent public displays of faith. I do agree that the government should not do anything with taxpayer money to support any particular religion or religious group (for sacred purposes, anyway; if you want to support religious organizations feeding the hungry out of church basements that's something we could discuss).