No, not the way you are presenting it. The language is quite specific and clear: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof".
The US Supreme Court has clarified even more explicitly in it's recent Ruling Galloway V the Town of Greece what the state may or may not do:
1. The state may not compel or coerce one to engage in any religious practice or ritual.
2. The state may not interfere with any individuals voluntary engagement in any religious practice or ritual.
2. The state may not endorse any specific religion religious practice or ritual.
3. The state may not disparage any specific religion, practice or ritual.
You bring up debates about moral questions - which do not include and specific religious practices or rituals. What about the examples of the state engaging in or compelling specific religious practices or rituals?
Feeding, sheltering and clothing the poor are explicitly called for as part of the practice of Christianity. I notice you are not complaining about the food stamp program, or welfare, or section 8 housing or any of these other Christian practices government is involved in.. Why not if you are a staunch advocate of separation of Church and State?
Honor they Mother and Father (take care of your elderly parents) is one of the 10 commandments. I notice you are not complaining about Social Security compelling people to obey this commandment.. why not if you are a staunch advocate for separation of Church and State?
The Christian Religion is explicitly against racism and sexism. (Where there is neither Greek nor Jew, Bond nor Free, Male nor Female but Christ is all and in all). So why are you not up an arms about all the laws against discrimination when that an explicit Bible teaching?
Seems to me you have no problem with the government engaging in religious practices (and compelling the tax payer to pay for those practices) when you agree with those practices. You only have a problem when you don't agree with those religious practices... If you were truly committed to your version of Separation of Church and State you would be staunchly opposed to Welfare, Food Stamps, Medicaid, Section 8 housing, Social Security, Desegregation, Equal Rights laws, tort laws, adoption laws and many other Federal and State laws which are found in the Bible some of which are specifically religious practices!
Since you are not rising in opposition to these laws which can be pulled right out of the Bible or are actually part of religious practice but you happen to agree with, then it is clear your Separation of Church and State objection is not about the principle of Separation of Church and State but about you using the argument selectively for those things you don't agree with.