The Israelites had intermarried with people who did not worship their God. This was a violation of what God told them to do because He knew that if they did their hearts would turn away from God. He was absolutely right. This is why it is so important for a Christian to marry someone who shares their faith and values. If God is the most important thing in our life we best find someone to spend our lives with who also makes their relationship with God as the most important thing in their life. The Bible is full of examples of how disregarding this wisdom leads to trouble. We also have likely seen this in the lives of people we know as well.
Ezra was not guilty of this sin. Yet, when he prayed to God for mercy on behalf of Israel, he did not separate himself out. He didn't say their sins and their guilt. He says "our" sins and "our" guilt. He didn't look for ways to make himself stand out from the group or point to him doing right while everyone was doing wrong. He said I am part of Israel and as a nation we have fallen. The decisions of some impact the whole group. This is also similar to what happens in church today. A person who lives in sin will affect the whole congregation. Our private lifestyles have an impact on our churches whether we think it does or not