Form 8615 requires me to fill in my parents' ssn (which they don't have because they are foreigners). I searched online and it seems like I can only print them out, write NRA by hand and mail my tax return. However, since I live in New York, it seems like New York State requires income tax return prepared using softwares to be filed electronlically. TurboxTax won't let me e-file without a "proper" parents' ssn, so what should I do?
You cannot e-file a state return if the federal return cannot be e-filed. So you mail the return to New York.
New York prefers e-filed returns, but there are certain circumstances that make it necessary for you to file your NY return by mail and the state DOES allow mailed returns. If you could not or did not e-file your federal return then your NY return cannot be e-filed. It has to be mailed. It is not possible to e-file any state return if the federal return was not e-filed and accepted by the IRS.
https://www.tax.ny.gov/pit/efile/efile_mandate_for_individuals.htm