'It's the big question of separation,' said the Stirling Labour group leader, Corrie McChord, when asked why he was unable to form a coalition with the SNP – a party which he accepted had almost identical social policies to Labour.

Now, I may be missing something here, but I wasn't aware that Stirling Council was in danger of separating from the United Kingdom. Why the independence referendum should have had such a decisive bearing on who runs council refuse and leisure services in Stirling is not entirely clear. Perhaps Labour believe the Nats will put something in the water or plant separatist propaganda in the wheelie bins.

Whatever, it seems that Labour think they have more in common with the party that wants to privatise most council services than the party that wants to use them as a bulwark against the austerity plans of, er, the Conservative-led Coalition in Westminster.

And it is the same across a wide range of local authorities. In Aberdeen, where the SNP had great hopes, a devil's alliance between Labour and the Conservatives has locked the Nationalists out of Scotland's oil capital. Meanwhile in Stirling the SNP was the largest party and the Nationalists thought they were a shoo-in until Labour and the Tories fell into each other's embrace – bet Lord Forsyth never expected that. Falkirk and South Ayrshire have also fallen to the new Labour-Tory axis, leaving Keir Hardie, the founder of the Labour Party, twirling in his grave.

Is this municipal opportunism at its worst, or are we seeing a new Unionist alliance forming in Scotland? It's a high risk, certainly. The Scottish Liberal Democrats were all but wiped out last week as a result of their entering the Coalition with the Conservatives in Westminster. What makes Labour think they can avoid the same fate now they are in bed with the Conservatives in so many Scottish town halls? "Vote Labour, get Tory" is the SNP's new post-election mantra. The Nationalists can hardly contain their frustration that so many councils have slipped from their grasps after an election which they hailed as a "historic victory".

It's all about tribalism, of course: the historic enmity between Scotland's two great political parties, Labour and the SNP. The independence referendum is largely irrelevant to what happens in Scottish local authorities. But Labour and the SNP will move heaven and earth to find reasons not to recognise what is blindingly obvious to most observers: that on the entire range of policy from job creation to the running of public services, there is hardly a blade of grass between them.

Only in one city has tribalism not prevailed: Edinburgh, where a Labour-Nationalist coalition is to run the capital. Why so different? Labour's leader, Andrew Burns, did his best to cobble together a Tory grand coalition "of all the talents" but it seemed a bridge too far for many in the Edinburgh Labour party, and for the smaller parties, such as the Greens, who made clear they would never support such an alliance. But I think Edinburgh will be worth watching because, improbable as it might sound today, such a Labour–SNP alliance may be the future for Holyrood.

Yes, the idea of a coalition between the SNP and Labour in the Scottish Parliament sounds as likely as Rangers and Celtic fielding a joint team for the European Cup. That doesn't mean it won't happen.

Let's say for the sake of argument the SNP has lost the 2014 independence referendum – that's what the opinion polls predict, after all. Independence is off the agenda, and the SNP is licking its wounds. The cybernats are hunting the blogosphere for quislings and fifth columnists to blame for duping the Scots into voting to remain under the heel of the English jackboot.

Now, this would be a setback for Alex Salmond, or possibly Nicola Sturgeon, who might be leader by then, but it wouldn't necessarily destroy them politically. As we know, most Scots voted SNP in the 2011 landslide not because of their policy on independence but because they seemed to be the best bet for running a decent administration in Holyrood. So the SNP goes into the 2016 Holyrood elections battered but unbowed. The Liberal Democrats are still pole-axed because of their Coalition with the Tories in Westminster, who have just been re-elected in the 2015 General Election. Labour is on a roll in Scotland because of the referendum result and is appealing to Scots to vote for them to continue the fight against the Tories in Westminster. The SNP will not be able to repeat their landslide of 2011 in 2016. Which leaves Scotland in what might be described as an Edinburgh situation: both Labour and the SNP do well but are unable to form an administration on their own.

Now, Labour or the SNP tribalists might try to court the Tories. But they would rapidly realise that the voters, and their party members, simply wouldn't have it. Labour would just have emerged from an election where they had promised Scottish voters that they would defend them against the Conservative Government in Westminster, so they could hardly go into coalition with them in Holyrood.

The SNP or Labour might be tempted to run a minority administration as the Nationalists did in 2007. But it's worth remembering that, towards the end of the 2007-11 SNP minority Government, they was unable to do anything, even introduce minimum pricing for alcohol, because it lacked a stable majority.

The truth is that, in a parliament of minorities, if you want to govern effectively, and ensure that your legislation is put in place, a coalition is the only way to do it. Labour and the SNP would discover that, with independence now off the agenda, they actually agree on so many issues – growth versus austerity, welfare reform, extending Holyrood's powers – that their best bet is to swallow their pride and deal with each other.

Indeed, Labour and the SNP might realise that tactically they have no option but to co-operate. That's what happened in the Welsh Parliament where Plaid Cymru and Labour ran out of reasons not to work together and formed a coalition in Cardiff in 2007.

And what happens to Tory-Labour councils like Stirling? Well, everyone makes mistakes.