Yes, it will weaken the dome. But, you may be able to mitigate the problem in other ways.

You could tighten the bolts down in the dome (I never do in a complete dome) and that helps somewhat... to a point.

I've seen some clever doors in domes.

Bad Idea Theatre uses a clever idea. It helps.

They take a hexagon on the side of the dome and do something like this:
_
/| |\
\|_|/

I don't know if the above will look good in tribe, but the concept is to take the top left vertex of the hexagon and connect it to the bottom left vertex with a two-piece vertical strut. It is two pieces because in the middle of that vertical strut, there is a short strut that connects to the left vertex of the hexagon. Same thing on the right side. The vertical strut is actually two struts that meet in the middle with a short horizontal strut that is attached to the right side of the hexagon.

The end result is a rectangular door. It is marginally better structurally than leaving a strut out, but it is much better than the typical missing strut door because it has vertical walls and a flat bottom, so people don't trip and fall on their way in.

We used the information on Earl's webpage to modify the geometry of our 2v and 4v domes to make a larger entrance without significantly impeding structural integrity. This seems to me like the proper way to do it if you're worried about the stability factor (i might be if i was hanging hammocks or people on the inside). It moves the center point of one of the hexagons upward to make one triangle about 6.5 feet tall. For a 3/4" EMT dome, 1" EMT should be sufficiently strong. We used 1.25" EMT for the long struts of the entrance of our 4V dome but it was expensive and probably overkill. We used 1" EMT for the entrance on our 2v dome and it seems plenty strong.

dome.zillabit.com/geometry.html

(math skills recommended)