You're both right and wrong at the same time.
The Church is not Israel, but neither is modern Israel the same as ancient Israel.
The modern state of Israel is also not a Jewish state. There is no state religion, just like in the US.
It's a fine line my friends and I have discussed for decades, but, as I have had to concede in the end, the line is clearly drawn. Those who believe in Jesus and keep the commandments are the family of Jesus and children of God. If Israel ever starts keeping the commandments, the door will be open to return. They aren't bearing the fruit as of now, however.
There has almost always been division among the descendants of Isaac and Jacob as a whole, as to whom they should serve.