Air carrier flight crew reported the magnetic compass was not indicating correctly during climb. ATC issued a direct heading to a fix and the crew continued the flight.

Narrative

We were taking off runway XX at ZZZ airport. While taxiing and parallel with runway XX; I instructed my FO to do the procedure for runways with magnetic anomalies as stated in the manual. My FO put in the reciprocal heading of runway XX while in DG mode; matching the heading on both PFD's (Primary Flight Displays). We were cleared to take off runway XX with no delay. On the roll; with my thrust set; heading checks" call; I noticed that my heading was maybe 5 degrees to the right of runway heading. After take off tower instructed us to make the right turn and switch over to departure. I checked in and as I was rolling the heading bug over to 355; I stopped about a 340 heading when departure questioned the heading we were given. Departure gave me a 320 heading instead. I was checking both PFD's and the MFD (Multi-function Flight Display) headings in comparison. Something was not quite right on the gyros and AHRS. The standby compass was stuck in a 360 heading and wouldn't move. I had put the switches from DG mode back to MAG (Magnetic) mode trying to fix it. They turned us to a due west heading and then gave us direct a fix. We had no trouble going directly to a fix. No issues after that. I called departure once at the gate at our destination and explained to them our company procedure regarding known magnetic anomalies. They said when I was turning to a heating of 355; they showed me at 040. When given 320; they showed me at 020. Our PFD showed the correct headings. Cause: Maybe the magnetic anomaly procedure was a little off on the heading or done incorrectly? Suggestions:I think this is an unsafe procedure and that we should keep the aircraft in MAG mode during take off. The EFIS (Electronic Flight Instrument System) comp mon caution goes away once take off is complete."