Possible Solutions For the S.H.I.V. Doorway Bug[]
Considering it's 2015, and the developers are already well on there way to creating the next XCOM, it's highly unlikely this bug will ever get fixed offically. Therefore it may be worth considering placing on the page some ways to circumvent this bug:
1) Don't put your S.H.I.V. near a doorway. A silly answer but it's the best solution.
2) Blow up the doorway (or a wall attached to the doorway) with explosives, find an alternate route, go to the evac point, or abort the mission. Note: This solution will really only help you on common maps because large doors like those found on the Temple Ship (the final stage) are indestructable.
3) If you're stuck on the Temple Ship, there is one unique trick you can do here - kill your volunteer. When your volunteer dies the game actually gives you the option of restarting this level again, exactly how you began it (as for why this is I can only theorize the developers intentions). There are few things in this game that can deal friendly fire: grenades, shredder rockets, regular rockets, and even your psionic's own rift ability. If your only option is to use rift, which has a five turn cooldown, remember that you can press the backspace button in order to quickly end turns.
4) If you're playing on iron man setting, and you accidently placed your S.H.I.V. in front of an unopened door, and you haven't ended the turn yet, try to end task the XCOM program via task manager (i.e. press ctrl + alt + delete). The autosave only kicks in when you end your turn.
5) If none of the above work, and you're not playing with the iron man setting, try reloading a previous save before you encountered the bug.
In addition, I haven't read this happening to anyone else, but when I accidently activated this bug on the Temple Ship the game actually locked me out of three doors, all of which were necessary for me to continue the level (right after fighting the waves of Floaters); even though my S.H.I.V hadn't actually been anywhere near the the other two doors.
Anyway, I hope this information helps someone --- random anon