Our boxes used Glenair Might Mouse series 805 connectors. We didn't have any evidence of problems arising from the non-Ethernet connector (impedance bump, crosstalk).
The problems we DID have were the following:
1) silly wiring errors
2) selecting cable and crimp pins (gauge)
3) ensuring 360° shield termination
4) sorting out the "RJ45" (8P8C) end
Surprisingly, somewhere out there is an alternative Ethernet wiring standard that is different than T-568A and it isn't the expected cross-over nonsense. It's another 8P8C pin/wire colour assignment that results in Channel C being wired backwards ( + <> -). I can't even explain its existence.
Another thing to worry about is scrambling the twisted pairs such that the continuity rings-out 'correct', but the pairs are scrambled up. We worried about this enough to avoid it.
All these silly wiring problems can be avoided if you have one person designing the entire path, end-to-end. And make the associated drawings ultra-detailed (specifying every possible detail, even to the point of providing redundant info as a built-in cross-check).
Obviously select cable to match Cat5/6, and then choose the connector and crimp pins to match the wire gauge.
Wiring inside the box(es) should pay attention to the Cat5/6 requirements.
Terminating the cable shields with neat 360° shield termination, as opposed to a ground wire pigtail, is something our E3 guru demands (and we respect his opinion highly). But it takes some effort to implement it.
And if you have 'RJ45' (8P8C) connectors in the system, then you may be tempted to use fancy RJ45 connectors with an embedded shield that grounds itself at the (for example) laptop end. Make sure the connector actually fits the device before you bother. Same thing with those silly RJ45 boots; they look silly shoved half-way up the cable because they don't fit.