Impedance matching components with Ethernet
I designed a two gigabit Ethernet ports with bypass board almost two years ago.

You have miss just one thing with impedance:


Ethernet lines are differential pairs with a differential impedance of 100 Ohms
Your relay is single line with characteristic impedance of 50 Ohms


But in your differential pair, each line will have its own characteristic impedance, lower than 100 Ohms but higher than 50 Ohms (for instance a quick computing in Saturn PCB give me 77 Ohms for line characteristic impedance of a 100 Ohms differential pair).

So yes you will have an impedance mismatch but so have you when you have a via, a pin, a connector, and also when you have no ground reference on your Ethernet pairs between transformer and connector.

A little impedance mismatch is not a big deal, this will distort your signal but really I don't think you will be able to find it.

I will be more worried by the maximum cable length for your bypass than by this impedance issue.

Here is an extract of the schematic of the board I designed:


We used more general use relays (insertion loss = 0.33dB @ 900MHz), but cheaper.