Bitcoin Core is really more of a process and a community than it is any specific group of people. There's no set criteria for "being a Core dev" - it is simply the set of people who discuss on the mailing list, send patches to GitHub and participate in the consensus-building process. In my experience, the influence of community members grows organically based on technical competency, domain expertise, track record and personal trust relations between community members - not on some appeal to authority or an organized hierarchical power structure.

The decision making process is based on an IETF-like[0] consensus-driven approach, where a very high threshold of rough consensus within the technical community is required for making changes to the protocol. This hardens the protocol rules and helps protect the development process from hasty decisions, political forces and tyranny of the majority situations - with the price of a slower development process and reduced innovation. Overall, I personally think that stability and resistant to change are good things, and prefer to be wrong on the side of defaulting to no-op when there's no consensus, rather than be wrong on the side of making harmful changes.

[0] "We reject kings, presidents and voting. We believe in rough consensus and running code" -- David Clark, The Tao of IETF https://www.ietf.org/tao.html