This would be my argument for allowing people of various religions to take their religious holidays, but not require everyone to take them (if they don't want to).

So (and these will all be hypothetical because my knowledge of holidays across various religions is pretty poor -- sorry) :-

Imagine there are four main religions in the UK -- Potterism, Everdinery, Swannism and Sherlockian.

Potterism celebrates the 31st of July, 31st of October, the 2nd of May, the 1st of September and the 19th of September as its holy days.

Everdinery celebrates the 10th of March, the 20th of May, the 31st of August, the 9th of January and the 5th of July.

Swannism celebrates the 3rd to the 5th of May, the 10th of August, the 12th of September and the 12th of December.

And Sherlockian celebrates the 1st of February, the 9th of March, the 12th of June, the 24th of September and the 10th of October.

Along with all these, all four religions celebrate the 31st of December, the 1st of January and the 23rd of August. Just because.

(Really making this up as I ago along).

The celebrants of each religion can take their days off as a holiday (without using up their paid holiday allowance), but businesses do not have to close. Bank holidays become a thing of the past.

Schools ignore them, and school holidays are arranged around more sensible times (summer holidays, spring holidays, winter holidays).

Religion is taken out of public life more or less altogether.

Now I accept that in "real life" this will be more complicated, but businesses can adapt for Jewish, Muslim, Christian and other workers and would not need to shut down on such a wide scope

The only exception might still be Christmas, because that has become more of a secular thing than a religious one.