I just put this 5 speed into my formerly auto car and the shifter and the housing is off to the right. Is there any harm to this? I should note I haven’t yet installed the transmission crossmember adapter I got. I also undid the motor mount bolts from underneath, would that have caused it to slip out of alignment?

 

I would say something is out of alignment. Recheck the cross member, transmission bushings and motor mounts. Compare yours to photos in this link: https://www.rx7club.com/2nd-generati...shings-637191/ Are you using the correct cross member (https://www.atkinsrotary.com/store/T...ission-Mounts/) ?