So basically I created a shape where the Fill is separated from the Stroke. The Fill has a lesser transparency then the Stroke.
Up close they look seamless without any gaps but when zoomed out or when exported to a bitmap, there is a 1 pixel gap between them.
If I combine the two shapes then one will take on the same transparency as the other which is not desired for what I'm trying to achieve.

Any ideas on how I can make the two objects join seamlessly without compromising their transparencies?

Here's what it looks like:

Hhhm, you're talking about the gap between the inner circle fills and the outer circle strokes? And not the gap between the 2 side-by-side circles, right? If I understand correctly this gap is caused by the way Inkscape automatically adds antialiasing to certain objects. If the objects did not contain transparency, you could fix it by making either the inner circles slightly larger, or the outer circles slightly smaller (or having a wider stroke). I think the most proper way would be to make the inner circle fills slightly larger.

But since they contain transparency, it will be incredibly difficult to make them fit precisely with no gap and with no overlap. (Because if they overlap, it will create very thin darker circle.) It might even be impossible.

Would it be possible, instead of using transparency, to make them shades of gray? Then you could make the inner part slightly larger, so that they overlap, and the overlap would not be noticable, because they would now be opaque.

The only way I can think to do it is to make the object two circles instead of one. You can do a path/difference if you don't want to have the larger object affect the translucency/color of the inner one.

That was going to by my answer too, until I realized that both parts are partially transparent. So anything underneath or above the other will be a different color/alpha value, and therefore be noticable.

Well unfortunately I haven't been able to come up with a method around this but I'll just increase the inside by one pixel. Not perfect but better then nothing.