Is the behaviour of .* to include . and .. defined in LSB or POSIX or some other specification?

Quoting from the Single Unix specification version 2, volume ”Commands & Utilities", §2.13.3:

If a filename begins with a period (.) the period must be explicitly matched by using a period as the first character of the pattern or immediately following a slash character. (…) It is unspecified whether an explicit period in a bracket expression matching list, such as [.abc] can match a leading period in a filename.

There is no exception that would make the second period in .., or the empty string following the only period in ., not matched by the wildcard in .*. Therefore the standard says that .* matches . and .., annoying though it may be.

The passage above describes the behavior of the shell (sh command). The section on the glob C library function refererences this passage.

The language is exactly the same in version 3, also known as POSIX:2001 and IEEE 1003.1-2001, which is what most current systems implement.

Dash, bash and ksh93 comply with POSIX. Pdksh and zsh (even under emulate sh) don't.

In ksh, you can make .* skip . and .. by setting FIGNORE='.?(.)', but this has the side effect of making * include dot files. Or you can set FIGNORE='.*', but then .* doesn't match anything.

In bash, you can make .* skip . and .. by setting GLOBIGNORE='.:..', but this has the side effect of making * include dot files. Or you can set GLOBIGNORE='.*', but then .* doesn't match anything.

Probably you mean the functionality in bash expansion about globignore. By default the bash expansion match . and .. but reading the man:

The  GLOBIGNORE shell variable may be used to restrict the set of file names matching
   a pattern.  If GLOBIGNORE is set, each matching file name that also  matches  one  of
   the patterns in GLOBIGNORE is removed from the list of matches.  The file names ``.''
   and ``..''  are always ignored when GLOBIGNORE is set and not null.  However, setting
   GLOBIGNORE  to  a non-null value has the effect of enabling the dotglob shell option,
   so all other file names beginning with a ``.''  will match.  To get the old  behavior
   of  ignoring  file  names beginning with a ``.'', make ``.*''  one of the patterns in
   GLOBIGNORE.  The dotglob option is disabled when GLOBIGNORE is unset.

You can set the variable GLOBIGNORE=.:.. so when you tipe something like this:

rm -r * .*

you are removing only the current directory. The POSIX standard only specify that . is the current directory and .. in the parent of the current directory. The special meaning of .* is interpreted by bash or other shells (or programs like grep).