For an example of this, see non-compete clauses, for most types of employees in California.
For example, many types of racial discrimination are technically illegal in many EU countries. But look at what actually gets enforced, it's unfortunately made to look like a huge joke.
(a) The EU can make "Regulations" which come into force as laws in each member state. But those are rare.
(b) ... The more common form is "Directive", and member states are legally obligated to implement into national laws. This is effectivly "EU law".
(c) ... membership of the EU, also requires membership of the Council of Europe, and European Convention of Human Rights, and European Court of Human Rights, who can make judgements against a member state to force them to do things.
The problem with that specific topic is that it can be very difficult to prove discrimination; also, legislation can pave the way but it's up to people to actually walk it. It's the same in some US states, really, and elsewhere is usually much worse.
Generally speaking, EU Directives (which must be implemented in local state law) are respected, and they can be vigorously enforced when people appeal to them. Like all laws and tribunals, EU ones are not perfect (some countries just ignore contrary verdicts, preferring to pay continuous fines; and some bad local laws are not appealed against nor closely scrutinised), but they are better than the alternative anarchy. Most EU directives did an inordinate amount of good for "retrograde" countries (Italy, Spain, Ireland, Britain etc), but sometimes it takes a generation to appreciate changes in law.