Should CX teams and Product Management teams be on the same team? Pros/Cons?
If by CX you mean Customer Experience, then by experience I value them to be in the same team as PMs.
One of the secret for great products is to look for collapsing the stack, have closer relationships between all the functions. Having customer support close to the product teams helps to make sure that PMs are always close to customer problems, but also ensure faster resolution.
There is nothing inherently wrong with having someone with a title "product manager" reside on a CX team. The caveat is depending on what the expected scope of that PM is, they may not be set up for success, or they even may be playing a role that (unintentionally) puts customers at a disadvantage.
Situations when it's good to have PMs be a part of CX org:
They help build internal tooling for CX or integrate company's own product and CX internal tooling in ways that helps teams better understand customers and ultimately, serve them better
The product offering of the company is in the CX market, and that PM team is a "skunkworks" unit driving experimentation and dogfooding of the company's product leveraging own CX team as customers
These PMs act as outbound PMs focusing on collecting, summarizing and distilling customer needs into specifics requests for other product teams, thus saving time and effort on research and holistic discovery around new capabilities
Situations when it's NOT good to have PMs be a part of CX org:
It's a move to get the overall PM org "closer to customers" instead of finding a way to incorporate customer centricity into all PM practices and rituals
Overall "nesting" of PM org within CX - this will most likely rebalance incentives on customer renewals and focus roadmap on addressing (often tactical) customer asks, depriving the organization from an ability to build and execute on a bolder product strategy, leading to business disruption and ultimately, loss of innovation/customers