Parkin saw red in stoppage time, but York were full value for their point.
Vadaine Oliver was twice denied early on by Jake Cole, while opposite number Kyle Letheren got in on the act by blocking Shamir Fenelon’s close-range effort.
North Ferriby were left frustrated as Macclesfield returned from Grange Lane with a comfortable 2-0 win.
After 17 minutes, however, defender George Pilkington came up from the back to head the Silkmen in front from a set-piece.
Within a few minutes Chris Holroyd flicked on for Danny Whitehead to fire past Rory Watson and put the visitors firmly in control.
FC Halifax Town were held 0-0 by Stockport County in National League North, while Harrogate Town lost 3-1 to Gainsborough Trinity.