They are signing non-Basque Spaniards for the last 20 years. Ofc majority of their players are Basques as they come through their academy or are signed from smaller clubs in the region. Some of them like Remiro are also from Lezama (Bilbao academy).
But just in current squad they have a Catalan Sergio Gomez and a Galician Brais Mendez and before that they had David Silva (Gran Canaria) and Canales (Cantabria). Just out of my head, there are surely other players too.
E: Slowpoke, I see
@Andresito already mentioned Silva and Canales.
Merino was born in Pamplona as was Raul Garcia for example. But Bilbao considers players from the Navarra community as eligible to play for them, probably because Basque is official language there besides Spanish.