Why should even the tiniest minority of a population be subjected to religious rules they don't subscribe to?

The religious origin of the law is irrelevant. A vast majority of laws originated from religious viewpoints. Furthermore, any reverse is the same. If the ban is not implemented because atheists don't like it, then religious people are being subjected to religious rules they don't subscribe. In this situation, whatever will put out the least amount of people should be applied, so if in 50 years time atheists are the majority then bans on religious icons would be justified.

This is the most ill-conceived notion of democracy - just because a majority of people hold a certain view does not mean that minorities' rights can be infringed

Firstly, yes it does. That's how democracy works. Even in a fully direct democracy, some people are going to be put out by the laws that are passed. Take laws that protect workers by limiting work hours and enforcing certain standards of safety. This infringes the employers right to freedom of contract, but society shares that's fine because a majority believe worker safety is more important than corporate profits. The same logic goes into laws that restrict the drinking age to 18 or 21, the age of consent to 18 in the US and movie and game restrictions.
Secondly, in western democracy we attempt to limit these infringements by making it so that serious breaches can only be justified in exceptional cases. Not being able to drink out on a Friday is not a serious breach. You can drink at home if you want and a night off from alcoholism isn't going to hurt you. In addition, if the ban was supposed to aid the moral state of the nation that is a valid justification according to the ECtHR.

Any state governed by the rule of law has an obligation to uphold the rights of all its citizens especially against majority discrimination.

People much smarter than you and me have already discussed this at great length. Instead of the tyranny of the majority, you are advocating for the tyranny of the minority, in which the will of the majority is restrained to protect minorities. This is resolved quite simply through checks to the power of the majority, not the transfer of power to the minority to block any laws they disagree with. This also touches upon what I said above, namely that this ban is not a serious infringement of rights. I also wonder whether you disagree with Good Friday being a holiday? Should everyone go to work to avoid imposing a religious view on others?

But the reasoning for this law is purely religious.

As I mentioned above, it could be classed as a law protecting the moral welfare of the state or one which aims to improve national cohesion through the maintenance of tradition. Unless the legislature explicitly said "this law is law because our religion tells us so" we can't say for sure and, while it may seem obvious in this case, there is room for ambiguity.

A religious argument has no place in the legislation of a secular society,

Of course it does. If a religious person is able to take part in the passing of laws in society, their religious views are going to affect the proposals they make. You can no more separate a person's religious beliefs from their opinions than you can the effects of their economic situation.

this would be a violation of the secular principle.

Not drinking on Good Friday does not amount to the state intervening in your religion. You don't have to accept God as the almighty creator or that Muhammad is the true prophet of Allah. You don't even have to stop drinking and, best of all, if you don't like it you can complain. There is not a single part of this that forces you to be Christian.