Online propaganda detection pipelines expose measurable privacy risks at multiple stages including data collection, feature extraction, and model inference. We conduct a structured analysis of $162$ peer-reviewed studies and formalize the problem using the Propaganda Risk Online Mitigation and Privacy-preserving Tactics (PROMPT) framework. PROMPT models risks $R$ and mitigation strategies $S$ through a mapping $M: R\to S$ guided by a utility function $α\cdot \mathrm{PrivacyGain}(s_j) - β\cdot \mathrm{PerfLoss}(s_j) - γ\cdot \mathrm{Cost}(s_j)$, with tunable $(α,β,γ)$ enabling stakeholders to balance privacy, accuracy, and deployment costs. To assess practical adoption, we introduce a compliance score that quantifies the alignment of existing methods with GDPR, CCPA etc. requirements. Our evaluation shows that many widely used pipelines remain non-compliant, particularly in metadata handling and user-level aggregation. We further present empirical fine-tuning experiments on transformer-based encoders and decoders under synthetic perturbation, demonstrating a monotonic privacy-utility trade-off: with $q = 0.05$ performance decreased by 1-2% F$_1$, while at $q = 0.20$ the reduction reached 13-14%. These results establish quantitative baselines for privacy costs in propaganda detection. Our contributions include a formal risk-to-defense mapping, a compliance-oriented auditing metric, and experimental evidence of privacy-performance trade-offs, providing a technical foundation for building regulation-compliant and privacy-aware detection systems.