Bastard is quite acceptable but, increasingly, as successive waves of scarcely educated folk leave school the original meaning is becoming lost.
Certainly, if I used the term " born out of wedlock " most wouldn't have a clue.
Illegitimate birth in terms of officialdom has always discriminated against the father not least because in the case of the mother there cannot be any doubt as to parentage whereas proving paternity beyond all reasonable doubt ultimately requires DNA testing. It was only in 2005 that the British authorities finally permitted equal rights to the father passing on nationality to their bastard, sorry, illegitmate children.