So it was, when they had heard the Law, that they separated all the mixed multitude from Israel. Nehemiah 13:3

This scripture would not fly today.

It was read in the Law of Moses no Ammonite or Moabite should ever come into the assembly of God, because they had not met the children of Israel with bread and water, but hired Balaam against them to curse them. However, our God turned the curse into a blessing. Nehemiah 13:1-2

This seems discriminatory to not include these two races of people in the worship service – at least under today’s thought.

Perhaps you think they were obligated to do it because they were under the Law and today we are no longer under the law. According to the writings of Paul that is correct – for you are not under law but under grace. Rom 6:14
But to simply take that part of the verse seems to take it out of context. Romans 6: 12-14 says, therefore do not let sin reign in your mortal body, that you should obey it in its lusts. And do not present your members as instruments of unrighteousness to sin, but present yourselves to God as being alive from the dead, and your members as instruments of righteousness to God. For sin shall not have dominion over you, for you are not under law but under grace.

It seems that not sinning is the message Paul wanted to get across. It is the same message Jesus wanted o get across in saying, “if your right hand causes you to sin, cut it off and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell.” Matt 5:30
That right hand might be a person that tempts you to sin. Perhaps you need to get rid of the TV, the Internet, or avoid a bookstore. If something regularly causes you to sin then cut it out of your life.

In the days of Nehemiah, the Ammonites and Moabites worshipped different gods than the true God of Israel. This acceptance of other gods is exactly what led up to the captivity. Nehemiah is determined not to repeat the same mistakes of the past.
Ungodliness should not influence Biblical principles or worship, therefore, he cut their influence out of the worship of God.