tl;dr: Technically yes, it's possible. Realistically no, you can't.
That is not within the abilities of OBS at present. You may be able to run two Portable versions of OBS at the same time (to prevent settings file write conflicts) if your system is capable of managing the encoding of two streams of that size simultaneously, and your network has the bandwidth needed to support streaming at the required bitrates.
Do be aware that video capture devices like webcams can generally only be used by one program at a time (and two copies of OBS count as two), and multiple captures hooking the same game/window/display will cause problems.
Chances are good that running two copies of OBS will not allow you to do what you want to do here.
About the only way I can imagine to make this work would be to run an intermediary server, do some deep-level geekery to rotate the video stream before sending it on to the 'other' aspect ratio end-point. But that's extremely involved, and we absolutely cannot provide support on the process of doing that here.
In short, no, that isn't possible.