Actually, Shepard being a biotic is easy to explain. The first recorded incident of humans encountering biotics in their own species was some time after the war between humans and turians. The incidents that caused the first few human biotics were accidents that costed many lives.

Kaiden was actually among the first human kids to be exposed too ezo and live on to actually use it in combat as he was born on the same year the first accident took place in 2151.

Shepard being a biotic can also be explained the same way Kaiden is. Shepard too was born on a year a biotic incident took place in 2154, 3 years after Kaiden.

The incidents that caused biotic kids to happen took place over 10 years of 2150-2160. At least the "accidental" biotic kids.

Alec Ryder could be perceived as the same age, if not a bit older than both Shepard and Kaiden. And since we do have a 1 year margin of birth for the incidents to occur, and it has been mentioned how young children can be exposed a bit after birth and become biotics, we do have a few years too squeeze Alec in there.

However the Ryder twins themselves having biotics can't be explained easily, or probably at all and is just thrown out there because gameplay.