Is the Karma theory an essential component of Buddha's teaching? Stephen Batchelor claims in several speeches and books that


Buddha never said the Karma and rebirth theory was true,
it is not important to Buddha's teachings, and
when he was a Gelug monk and asked for support for the Karma and rebirth theory, he didn't get any sufficient answers (despite the fact that Gelug Buddhists tend to focus on scientific methods of acquiring knowledge).


According to Batchelor, the Karma theory was a common worldview in India at the time. Siddhartha Gautama's contemporaries believed in Karma like we believe in the Big Bang theory and evolution. Neither of these theories can be proved or refuted with an affordable effort (in order to prove evolution for yourself, you need substantial knowledge of biology plus systemic thinking skills -- both of which are hard to acquire).

Also, neither of these theories affects the main purpose of Buddhist practice -- to reduce suffering. If tomorrow someone proved the Big Bang theory to be definitely true (or definitely wrong), it wouldn't make most of the people happier/unhappier than before.

However, the question about Karma theory affects the Buddhist practice.

If someone believes in rebirth, then they would spend most of their time meditating and preparing for the next lives. This is not just theory -- in some Buddhist communities advanced members spend almost all their evenings in the Buddhist center and almost every vacation on some retreat. It looks like they don't have their own life apart from this practice.

If someone does not believe in the Karma theory, they will focus on making the best of this life (which may be the only one we get). Buddhist practice is a means to live the one life one has as effectively as possible. Basically, you meditate in the evening in order to better achieve your personal goals during the day.

Is the Karma theory an essential component of Buddha's teaching or not?
There is no Buddhism without Karma. Paticcasamuppada (the Law of Dependent Origination) is all about Karma and it's consequences. 

Akiriya-ditthi is the false view or opinion of the inefficacy of action: That neither moral good nor moral evil action have any delayed consequences for anyone.

This wrong view was taught by Pūrana-Kassapa during the time of the Buddha.

Today also there are people like Pūrana Kassapa who spread such views. What is more dangerous is that instead of presenting such views as their own beliefs, they try to present them as the teachings of the Buddha and mislead many who are new to Buddhism.