I was told that NC residents had until May 1st to file taxes, so why can’t I file for an extension now?

You can file a NC extension here: https://eservices.dor.nc.gov/vouchers/d410.jsp

The IRS will recognize your automatic extension  to May 1 by your zip code.   It is too late to send an extension request--if you wanted that you had to do it by April 15.