I have Resolve Studio and use it every day, along with FCP. However if your machine does not crash or shut down when running Resolve, that proves nothing about FCP. The software load paths of different apps are intricate and generally opaque to detailed inspection. E.g, just capturing an application load profile for a few seconds using XCode Instruments can consume a gigabyte of data, and even that is a sampled incomplete view.
If your machine is shutting down or rebooting when running an FCP task, that is by definition a system layer issue. An app cannot cause that unless there is something wrong at the hardware, OS or device driver layer. It cannot be fixed at the app layer.
Many years ago before protected-mode operating systems, this was not the case. A buggy app in Windows 3.1 or Mac System 7 could easily crash the entire OS. Desktop operating systems of that era did not have hardware-based memory protection, with the exception of Windows NT. However that was 30 years ago.
Today if a machine running MacOS or Windows crashes when running a certain app, it is not the fault of the app. Rather it indicates a problem at the hardware, system configuration or device driver layer. Understanding that and focusing on the problem area will lead to a lasting solution.
For example you could try Resolve or Premiere Pro and maybe it would keep crashing, maybe it would not -- or maybe you will spend months learning that only then to find the machine crashes.
If your machine is shutting down, rebooting or freezing, there are possibly (even likely) MacOS error messages in the system log indicating a kernel panic or uncontrolled restart. It is that area that gives clues to the true problem. You could probably get good support on an Apple forum for MacOS or hardware issues.