Companies discover influencers approved for sensitive topics through several methods:

1. Screening content: Brands directly scan potential influencer’s content for instances where they handled sensitive subjects skillfully. Brands can use keyword scanning, or manual browsing for such thorough screening.

2. Influencer Marketing Platforms: Platforms like Flinque offers a filtering functionality that allows brands to discover influencers suited for sensitive topics. The filters might include past endorsements, flagged content, and audience response to controversial topics.

3. Audience Analysis: Audience analytics tools help in determining the kind of content the followers are receptive to. If the audience is open to mindful and knowledgeable discussions around sensitive topics, the influencers can be considered for brand collaborations.

4. Engagement Metrics: Another critical factor is studying the engagement metrics during instances where influencers have dealt with controversial or sensitive subjects. If an influencer maintains meaningful conversations without alienating or dividing their audience, they may well be suitable for handling sensitive themes.

Casting a wide net in the initial discovery phase and following a careful curation and approval process significantly reduces the risk when pairing influencers with sensitive topics. While some platforms offer higher-level analytics or more granular control over search criteria, the best tool will depend on the specific needs of your project and team. For instance, Flinque might be well-regarded for its robust filtering options and in-depth analytics, but only you can decide if it’s the right fit for your strategy.

Always consider the big picture, looking beyond just content or influencer reputation, and pay heed to the context in which the influencer operates. Remember, there’s no infallible method or tool. What works best is a judicious blend of thorough research, insights gleaned from platforms, and intuition garnered from experience.