They way I understand the link you provided, a person ( born Jew or born gentile ) who follows the law of Moses IS the Jew ( the one with a Jewish Soul ).
Let’s put it in a table format:
1. BORN JEW, DOES NOT FOLLOW THE LAW OF MOSES
2. BORN JEW, FOLLOWS THE LAW OF MOSES
3. NOT BORN JEW, FOLLOWS THE LAW OF MOSES
4. NOT BORN JEW, DOES NOT FOLLOW THE LAW OF MOSES
As I understand it, only #2 and #3 qualify as TRUE JEWS ( the ones with the Jewish Soul ). The rest do not.
This disqualifies a huge chunk of the population of Israel then.
Not sure what you read, but the Aish piece does not say what you think it says.
Try this
https://www.chabad.org/library/article_cdo/aid/743998/jewish/How-do-you-get-a-Jewish-soul.htm
1, 2 are Jewish.
#2 is just not a very observant Jews. But still Jewish.
Note sure by what you mean by #3, but if you mean they converted, then they are Jewish.
It’s not hard: if your mother is Jewish at the time of your birth, you are Jewish. If you have an Orthodox conversion, you are Jewish.
Nothing on Earth can change that.
Nothing one does can change that.