There are several things that are going on here and are probably confusing you a little. One thing is, that whatever instructions given to Popen will be executed in the child process and will not affect your main process. You can merely Pipe or retrieve results from it.
First to comment on your second use case, where you use string as an argument. From the docs you can read:
class subprocess.Popen(args, bufsize=-1, executable=None, stdin=None,
stdout=None, stderr=None, preexec_fn=None, close_fds=True,
shell=False, cwd=None, env=None, universal_newlines=False,
startupinfo=None, creationflags=0, restore_signals=True,
start_new_session=False, pass_fds=())
...
args should be a sequence of program arguments or else a single
string. By default, the program to execute is the first item in args
if args is a sequence. If args is a string, the interpretation is
platform-dependent and described below. See the shell and executable
arguments for additional differences from the default behavior. Unless
otherwise stated, it is recommended to pass args as a sequence.
On POSIX, if args is a string, the string is interpreted as the name
or path of the program to execute. However, this can only be done if
not passing arguments to the program.
So in your second case, you are trying to execute a file or program x=y which doesn't go.
Even if you use list, like in your first use case, you must be aware, that this isn't equivalent to passing code to the bash shell. If you want this, you can use shell=True as an keyword argument, but this has other issues as indicated by the docs. But your code will execute with shell=True.
If your sole purpose is to set environmental variable, then you should consider the option to use os.environ variable that maps your environmental variables to values (as indicated by @cdarke first).