Safety first - Avoid this when playing against Sync, you will have a much harder time surviving BOOM! with a 3 card hand size. The same is true for Jinteki and Weyland IDs in general, most of the damage in the game is in one of these two factions, so the reduced hand size helps the corp to flatline.
Always Be running - Weyland has some of the biggest ice strength wise in the game, and they have very cheap ways to res this ice. Though neither side of this is as good as it once was, the runner lost e3 Feedback Implants and Weyland lost Oversight AI, Priority Construction still makes it very easy to rez space ice, like making Wormhole free. That click to break ability can help a lot here. That forced first run every can be a problem however, particularly against Jinteki due to traps that work in archives like Breached Dome or Shi.Kyū. When playing against Haas-Bioroid, particularly IDs like Architects of Tomorrow this can be redundant.
Neutralize All Threats - Like you said in your question, Controlling the Message punishes trashes, being forced to trash the first card you access can really make that hurt. Punishing trashes is starting to be more common in general, with cards like Wake Up Call, but CtM on the ID is worse due to consistency. There isn't much else ID wise that will let you know that trashing is going to be a bad thing.
Find the Truth - This one is relatively safe in general, no major upside, no major downsides with regards to the corp you face. The corp knowing what's in the grip shouldn't matter unless your deck has an unusual gimmick they will now know to play around, but knowing when it's worth making a run on R&D definitely can help.
For some matchups two of the directives are an issue, like you mention for CtM, that's why Adam needs Dr. Lovegood. Or perhaps he could pawn off his bad directives to Aesop. Just remember the good comes with the bad in directives, you can't just shut off the downside.
There are ways to play around these situations, For instance I've Had Worse or Beach Party can help offset the downside of Safety First, but for the purposes of this question we're looking at the corp, not the runner, and building around the objectives makes it harder to switch them based on the corp, Beach Party's click loss can really be an issue if you aren't getting the free draw from Safety First to offset, for instance.