Does Theravada Buddhism accept Jataka Stories? Once in a Dhamma talk I heard a Theravada Monk saying he did not believe in such stories, because some of them contradict the Buddha's teachings (suttas), I don't know if that was his personal opinion or a general view in Theravada Buddhism.
The Theravada accepts the Jataka stories as commentarial literature; they are not canonical, but are considered a reliable account by a learned Buddhist scholar. What are canonical are the verses that accompany the stories, as that is how 547 of the latter were easily remembered. Number of verses per varies; some have a single verse, others have over 100, I think.

It's not uncommon for modern Theravada Buddhists to question the authenticity of the stories, especially given their often fantastical content. Probably, though, it is more common for Theravada Buddhists to accept the stories far more at face value than they really should, again given their content.