Will an illegitimate child be admitted to Paradise, if they are pious or not, because they are perceived as an objectionable seed?
They will be admitted to Paradise, if they die as a Muslim. Being illegitimate has no effect on this, because it was not the result of their own actions; it was caused by other people. Allah (Exalted be He) says:
...and no bearer of burdens shall bear the burden of another.
Also, due to the generality of these Words of Allah (Exalted be He):
Every person is a pledge for that which he has earned.
Verily, those who believe (in Islâmic Monotheism) and do righteous good deeds, for them are Gardens of Delight (Paradise).
In addition to other Ayahs (Qur'anic verses) with the same meaning. As to what is reportedly related from the Prophet (peace be upon him): "The child born from Zina (sexual intercourse outside marriage) will not enter Paradise," this is not an authentic narration. It is ranked by
Al-Hafizh Ibn Al-Jawzy in his book "Al-Mawdu`at (Fabricated Hadiths)" as one of the Hadiths that are falsely ascribed to the Prophet (peace be upon him).May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.