In "Redemption", the legally elected klingon government (supported by most of the population) asked for federation help against, essentially, terrorists.The federation refused to interfere, because stopping terrorists is an 'internal matter'.
If this 'internal matter' was beyond the federation's authority, why should romulan help for the klingons be anything the federation can interfere with?
Now the federation can't interfere in internal politics, but has free reign to interfere in external politics (that do not involve it?)? What's the justification for this division?
Returning to this. The Klingon weren't fighting terrorists, the main reason the Federation stood back was that it appeared to be a conflict between two rival political factions, at that time the Federation (wrongly) thought it was in fact "internal."
Once the participation of the Romulans was made clear, then the long standing "Treaty of Alliance"
came into play. Part of the treaty was a mutual defense pact. Now Starfleet could get involved. Given Gowron's standing request for assistance, against what was now known to be a external force, there was no "hindering, obstructing, or impeding" of the Klingon government, there was no "interference."
Treaty of Alliance
What's the justification for this division?