I'm all for not judging a book by it's cover, but the fact of the matter is if we don't do that then we get stuck with an awful player for 25+ minutes more often than not (when a good group can run FBW in 18 minutes, dying after the objective in round 10). As much as possible I try to play with friends for this reason, but often we only have a group of 2 or 3. On the plus side, this makes kicking random players a lot easier.
I don't kick based on N7 alone, but it is definitely a factor, and will make me consider your class/loadout more carefully when deciding whether to play with you.
In particular, with a low N7 you must show me that you are trying to play one of the best possible characters--if you want to play something random I'll expect you to have extremely good guns (which likely comes with a high N7 rank, but if you've got close to level X rares I'll probably give you a chance).
With your manifest, I'd probably give you a chance as a Geth Eng, Sal Eng, or Asari Justicar using your Carnifex 3. If you unlocked Sal Inf I'd probably give you a chance with your Widow 1. I might not kick you with other infiltrators (particularly the Quarian, although Sabotage is often more annoying than helpful), but it would depend on my mood. If you played basically any other loadout (such as Widow 1 on a Geth Eng) I would kick you without hesitation. Similarly, if you are using Ultralight Materials on an SMG other than the Geth SMG, I will also kick you.
That said, even if I played one game with you, you'd need to prove to me you know what you're doing to not get kicked before the next game:
You need to be a team player and generally not just run around like Rambo.
You need to let the Infiltrator handle the decode objectives by himself, and not draw extra attention to him; on the other hand, if you are the only infiltrator you need to do the decode objectives yourself in a timely fashion.
You need to stand in the circle on hack objectives.
You need to use consumables appropriately--missiles in objective rounds at crucial times or if the party is near death, as opposed to just missiling a random prime for the hell of it.
If everybody else is suiciding after the objective in wave 10 to get to the next round faster, you need to do the same--regardless of whether you need the experience points or not.
You need to not die a million times far away from everyone else--when this happens, it's often easier just play with 3 people.
Assuming your character's main role is damage dealing (which is the case for most good characters besides a Salarian Engineer), your score has to be at least on par with the person in 3rd place.
You say you've succeeded on about 24/25 out of 30 fbw runs. This is actually not a very good completion rate. Good parties complete fbw essentially 100% of the time, and if I felt there was a chance of failure at any point during the match I'd absolutely kick the worst players on the team.