I just finished the Genetarr missions and can now sign the Alliance pact which would give me the ability to change to the Genetarr race. My question is simple can I only sign a pact with one of the other races such as Genetarr, Drannik, Zolzain, etc or can I finish every race mission and sign pacts with them all? I don't want to get stuck signing a pact with a race I don't really want.

You can unlock all the races. You're not stuck with the first one you unlock.

Plenty more to go. Genetarr and zolazin chains are the easiest to do but later on they will get more difficult.
Kronyn is short but requires flux probes
Mylarai is just plain long and needs resource probes at the end of it.
Lazuli and Drannik chains are supposed to cost a lot of energy but I haven't completed them yet.
Tatherian is the beast of the race chains but isn't available until much later on.

Xzien u missed out on xecti