The text within <> must be a 'simple scalar variable' in order for it to be interpretted as a reference to a typeglob, and not a shellglob. See the perlop manpage for more information.

To accomplish what you are trying to do, I recommend using the readline() builtin function that provides the same functionality as <> does:

my %opt;
$opt{'M'} = \*MF;   # You should use a reference here.
while (readline($opt{'M'})) {
    print "loop one...\n";
}
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Using readline() allows you to specify an arbitrarily complex expression, while still getting the same behaviour that <> does. For example, readline() also has the behaviour of wrapping an implicit defined($_ = readline(...)) around the readline().