Complex sentence: The decline was hastened by Stephenson's talking to the press in 1926--1927 about government officials who had accepted payments and bribes from the Klan; the organization's supporters became less able to defend it as law-abiding and upholding morality.
Split into simpler sentences: The decline was hastened by Stephenson's telling the press in 1926 and 1927 about government officials who had accepted payments and bribes from the Klan. The Klan's supporters were thereafter less able to defend it as law-abiding and upholding morality.