My thoughts too. Seems rather an abuse of the aims of HS&W provisions to use them to enforce uniformity.
I think your company is chancing it suggesting that "safety helmets might not fit.
You could have a policy that all long hair, whether men's women's, dreaded, straight, curly be tied up and tucked in as is common in clinical & immediate care, catering, uniformed services, construction and enginering construction settings.
I know many people with dreads in all walks of life; clinicians; doctors, nurses, paramedics, medical students, where one might think cross-contamination might be used as an excuse for discrimination, in food and catering...
in fact I can think of a few other people working with rotating equipment and condition monitoring who have dreadlocks. It's not common as hippies (the group of people I know most likely to sport dreads) don't generally get involved in oil and gas (where RE is most prevalent here), for some reason.
I know many more people with beard and peyos working in hospitals in Israel and in Magen David Adom, Zaka (founded by men with beards) and United Hatzalah where common sense is applied.
I (as a bit of a hippy student) had dreadlocks, still have a beard and worked offshore in uni vacations servicing and carrying out planned and reactive maintenance on rotating equipment in potentially explosive atmospheres.
I can't remember issues with face fit tests for the BA sets, smoke hoods etc but even back then industry tended to manage the hazards with permit to work controls, guards, lockouts, fixed fire and gas systems, portable gas detection, ventilation systems etc. I'm struggling to think of any situations where there were open rotating systems.
Now thinking about it, with a thicker layer of hair my hard hat stayed on more when I had dreadlocks than it does with my current short hair and a [scaffolders] hard hat with ratchet.
It begs the question what state is the plant in and what controls are there to manage rotating and gas hazards before they even become hazards to people with beards and dreads? As other posters have mentioned you should also be satisfying the safety controls hierarchy higher up elimination>substitution>engineering controls>administrative controls> ie guards, M&E lockouts, spindown before PPE> health monitoring.
I'm quite astounded to see H&S used for such possibly discriminatory purposes in T&T and would have though it would be more common here in the UK! I worked in an Embassy of Trinidad and Tobago in the 90s, BTW. I can check the law, there's a member of our shul from T&T who trained as a lawyer, though I won't see her for a few weeks.