"ideological influence" is correct and usable in written English.
You can use it to refer to the impact of an ideological belief or system on people, the government, or society. For example, "The ideological influence of communism was far-reaching and lasting."
This did not diminish his long-lasting ideological influence.
They hold no elected office and are accountable to no one, yet they wield immense ideological influence.
Some say that this time around, Mr. Khan is showing other signs of Iran's ideological influence, too.
Linking up with the Shiite Muslims of southern Lebanon was part of Iran's efforts to spread its ideological influence.
He didn't seem concerned about the ideological influence that the heads might have over his workers; he was more sheepish about having given up inventory for sentimental reasons.
This idealism is the legacy of the 60s and 70s counterculture, which continues to exert enormous ideological influence on Silicon Valley.
She cited both the black-power meetings she attended as a teenager and the bubble-gum feminism of the Spice Girls as ideological influences.
While McVeigh's ideological influences illustrate the potency of anti-Semitism as a political force on the American right, it dates back far longer.
The close relations of the Bourbons to France and the penetration of Central America by English traders, especially via their settlements at Belize and the Mosquito Coast, brought significant foreign commercial, administrative, military, and ideological influences.
What has changed is the now commonplace recognition, imparted in media studies and even in high-school English classes, that there's no such thing as neutral storytelling, and that every artistic composition, every visual representation, entails and embodies a wealth of ideological influences and prejudices which makes filmmakers want to stake out their positions clearly.
Switching Sides aims broadly at an educated American public, for whom Fels provides sound knowledge about the Salem witch hunt and leaves readers pondering the relationship between works of history and the ideological influences on the historians who write them.
