The European Court of Justice (ECJ) finding on Tuesday in two cases – one Belgian and one French – that private companies may dismiss workers for refusing to remove Islamic headscarves at work has come as an unfortunate boon to right wing election campaigns in the Netherlands, France and Germany. One French MEP tweeted gleefully that “Even the ECJ votes Marine”, after the EU’s highest court appeared to reverse established law from the European Court of Human Rights (ECHR), notionally Europe’s predominant human rights standards setting court, and important precedents in the US.

But the arguments about enforcing secularism that have riven France, in particular about headscarf bans, have crossed the political divide with much of the centre and left of politics also embracing laicité. The ruling in this deeply contested territory is far from a clearcut victory for the right.

And the court is nuanced. Companies can ban the scarves, but only as part of a general policy barring all religious and political symbols including Christian crosses. “An internal rule of an undertaking which prohibits the visible wearing of any political, philosophical or religious sign does not constitute direct discrimination,” the court said.

‘‘The rule,” it found, “ thus treats all employees to the undertaking in the same way, notably by requiring them, generally and without any differentiation, to dress neutrally.” And the business has to show that its policy is applied because it deems a policy of “religious neutrality” to be crucial to its business, with national courts deciding whether a company’s policy meets this difficult standard.

The court also ruled that employees could not be dismissed simply because a customer objected to dealing with an employee wearing a headscarf.

In 2013 the ECHR backed a woman’s right to wear a cross on her British Airways uniform, while the US courts have since 2004 required businesses to provide “reasonable accommodation” to staff to express religious convictions in their dress. In 2015 the US Supreme Court backed a prospective Abercrombie and Fitch employee who was denied a job because her dress did not conform with the values that the company was promoting.

If the Irish courts are asked to rule on which European court’s standards – those of the ECJ or the ECHR – prevail in our law if their respective jurisprudences conflict, the answer is unclear. We are signed up to both, although the ECHR’s writ is not directly enforceable in Irish law.

Nor is it clear whether the ECJ reasoning, notably its argument that employers must be able to show that a policy applies equally to all religions, would undermine the exemptions from discrimination law currently provided to workplaces run by churches. Employers proposing to exercise an expanded right to purge a workplace of religious manifestations would do well to tread warily.