As Charles mentioned you would be better off going with the PIC as a low-side driver, but the best route would be to use some cheap low-side driver like a BS170 MOSFET.
Switching from one PIC type to the next may not always guarantee it's going to work from one to the next if it's operating border-line.
And a quick look at the relay datasheet does not show they have internal diodes. You will for sure want a flyback diode across those relay coils.
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