In many cases, yes. A jewellery and loose clothing ban may be justified to prevent a potential hygiene hazard if you work in areas of food production or areas which need to be kept sterile.
Likewise, your employer can judge that loose jewellery may constitute a snagging hazard if you work with machinery. Your employer is responsible for your health and safety at work, so they need to be cautious in these areas.
If you think restrictions are not justified by health and safety concerns, talk to your workplace union rep if you have one, as they may know of solutions to the problem which other employees have used before.
Prohibiting loose jewellery such as a cross is likely to be justified on health and safety grounds in a clinical environment, even if the wearer wears the cross because of their religious beliefs.