Does your employer have to provide you with safety shoes?

Different companies & countries have different regulations.

In general the employer is responsible for the safety of its employees therefore he is legally (by law or for insurance) obliged to provide you with the necessary PPE. This can be either the actual equipment or an allowance to buy this equipment.

As the employer can be held responsible, he can refuse access to the workfloor/site if you're not wearing the necessary PPE.