It depends on what degree of "certainty" you are looking for. The only "variable" that affects radiocarbon dating directly is the variation in the amount of C14 being formed in the atmosphere by radiation from the sun, which is affected by the variation of the "solar constant". Cross-calibration of radiocarbon with dendrochronology takes care of most of that error for "more recent" dates (out to -10-20,000 years or so).
Most people who think carbon dating is "propaganda" are biblical creationists, trying to stuff their religion down the throat of science.
I would agree with the former, I would disagree with the latter. I'd also say there is a similar correlation to conservatives and those that say the "science" of global warming is propoganda.
Not a bad guess at all.