A properly secured Linux machine is a unicorn. The Linux desktop ecosystem is struggling a lot with putting software in namespaces. People still install software with their package managers outside Flatpak, there is no isolation of data, not to say many workflows depend on the whole user directory being available to access.
Not on any properly secured Linux machine. But yes, it's generally a bad idea to install software you don't trust, a category that anticheats slot nicely into, given their resistantance to auditing and analysis.