My camp has the same size dome as you guise and we removed a strut for a doorway as you are suggesting .
What we found was that the adjacent connections to the gap were more vulnerable (not significantly), but the next set out from those was fine. We used 3/4" conduit and had/have no intention of climbing our dome or hanging hammocks. So if you plan on climbing keep those weak points in mind because depending on the thickness of the conduit the struts may bend (which is not ideal and renders them useless for future use). We also added a second doorway
directly across the dome from the "front" door to access our more private camp space rather than go around the dome.
The only time removing a piece in this way could be "dangerous" is if you are planning on climbing the dome with a large amount of people (It would just end up damaging the struts via bending) and potentially cause someone to fall 5' if they anticipate a strut to be there and it's not, kind of like missing the last step but worse.
Note about climbing domes at all: Climb on the hubs as much as possible, avoiding the center of the struts which will bend and are a pain to replace, (especially if you fabricated the dome from scratch as we did). Do not allow people to hang from the dome unless the are holding onto a hub. 1" conduite in the absolute minimum thickness for climbing domes and even then I would recommend 1.5"-2". Thunderdome is a great example of this concept.
Another tip I have is to build the dome while keeping in mind that you will later take out that specific strut for the door, so don't put in on first in the connection for those hubs, because when the time comes to take it out (after you have built the full dome) it's easier if you don't have to "re-layer" the hub with all the pressure of the dome now present. We learned that one the hard way and had to loosen the next 2 adjacent connections to make it possible, then we had to take out the door, rebuild that hub and retighten the connections we had to loosen to alleviate the pressure. All that could have been avoided with more foresight like putting that strut on last in those particular hub connections. I recommend taking building the entire dome and then taking out those connections. Feel free to contact me with any other questions/need for support you may have.
[email protected].
Otherwise, I'll see you all on tutu tuesday to drink baileys out of boots

and make Old Gregg references.
In dust we trust.