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You try to discuss a constant, discrimination, by comparing a number of completely different things. It will get you nowhere.
What peaked my curiosity is that I don't think I've ever considered discrimination by comparison to it's application in different sectors. All to get to the route of why most people's gut is the coffee shop owner should be allowed to exclude children, but not say, groups of more than 2 Spanish people.
The egs you've just used are about safety. So the starting point is that you shouldn't discriminate, but that it's permissable where there is a safety or protection element in either direction - pedophiles in nurseries, or children in nightclubs, etc.
The difference with the coffee shop, is his rational is based on the fact he wants a certain vibe which children would prevent. Like clubs only letting in select people. But nether relate to safety - they start with freedom of choice. The freedom of a proprietor to choose how they run their establishment.
Yes, I am fully aware that the law is fluid, that was why I specified that age discrimination is legal in most countries in Europe. Germany, for example, has legal protection against age discrimination in the labour market/workplace, and there is every reason to think that similar legislation will be introduced in other countries. Or it might not.
However, your reasoning is off. You try to discuss a constant, discrimination, by comparing a number of completely different things. It will get you nowhere. For example, most countries allow some degree of discrimination against people with a criminal record. The state of New York is taking steps to limit this. Their case against this form of discrimination is made on the back of arguments such as the inalienable rights of the individual, the benefit to wider society etc. And of course one can point to a change in norms, such as a belief that people change.
But if one instead uses your line reasoning by saying "if you deny someone a job on the basis of a past conviction for shop lifting, how is that different from discriminating against the left handed?" then someone else can use the same approach to say "if a convicted shop lifter is allowed to work in a shop, then what's to prevent a convicted pedophile from working in a nursery?".