Will the use of Generative AI tools result in more or less trust in sales and marketing? I am curious how other companies' customers are responding to this content (i.e writing AI-generated prospecting emails or content on LinkedIn).

To keep or improve that trust there will need to a "human in the loop".  Gen-AI can accelerate and may need more strategic marketers with new skillsets to guide/shape outputs.

I recently encountered a significant issue with Meta’s Ad platform. While Meta’s thresholds utilize AI automation for efficiency, our thresholds were inexplicably reduced to just $2. This has made it challenging to maintain trust in Meta’s platform and continue our advertising efforts. The reduction in human support and the inability of the Meta Pro employee to manually adjust the threshold have added to the frustration. It’s crucial for Meta to ensure that their support personnel are well-trained and accessible for managing such a sophisticated platform. Without resolution, Meta risks losing valuable customers.

AI will help the creativity going and certainly be helpful. However, trust will not only come from a machine, for authenticity you still need that human touch

AI is just an accelerator.  How the final email, proposal, etc. looks before going to the client, and whether it speaks the language of the client's C-Suite (vs. vendor jargon) will increase the sender's trustworthiness.

Oh, I like this question. As Hannah A. mentioned, if the output quality is spot on, prospects will get a richer, targeted, and personalized experience. Building a good rapport with the brand/company. However, if knowledge of the use of GenAI or the sales reps are unable to continue the "personalized" experience via direct engagement (phone or in person), will become a double-edged sword. 
Definitely more to unpack but my initial thoughts on the matter.