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When the new company failed to secure the club's previous place in the Scottish Premier League,[80] Rangers were accepted into the Scottish Football League and placed in the lowest division, the Third, rather than the First Division as the SPL and SFA had sought.[81] The transfer of Rangers' SFA membership was agreed by the SFA upon acceptance of a number of conditions, 

Everything there points to Rangers being the same club. Not in the SPL, so enter the SFL instead, transfer the SFA membership not apply for a new one.
You idiots refuse to see the wood for the trees.

The irony is that they support a club that actually ceases to exist for at least a season and certainly long enough to miss out on being founder members of the league.

Yet they claim the history. Not so long ago one of the was banging on about being one of the original names on the Scottish Cup: yet it was a different club. Just shared a name. By their own logic of course. I wouldn't deny a diddy team one of their few successes