Regulations typically require the employer to provide all safety-related equipment. There is some variation, depending on the specific piece of equipment- and that can depend on the specific task.
"Safety rules" are not the only rules that determine the policies a company may follow. Labor agtreements, third-party certifications, and the general way the company operates affect such policies.
It's their company, but your life. It's quite possible that someday you will be placed in a position where you will have to choose between their opinion and your job.
