Considering the contact time and limited area, I don't think the material would be much of an issue. I'd be more concerned with cleaning products than structural material.

Less than 10% of new porcelain tubs test positive for lead. Take a lead test swab to the showroom if you are concerned.

Your old worn 80s tub may be a risk (have you tested it?) but a new porcelain one will not be.

I would also have the five kids, as well as yourself, tested for blood lead levels. You may find yourself very much relieved--stress and anxiety are certainly not healthy for anyone.

I am not surprised you had difficulty finding answers to your questions. Most
manufacturers are quite proprietary about their manufacturing processes and more specifically finishing processes.

Cast iron, fiberglass, acrylic, Vikrell
Cast iron tubs with enamel finishes are unlikely to contain lead unless they are old, were re-finished prior to the lead paint ban or are manufactured in China. (Not all Chinese made tubs have lead in them but you should be cautious).

I am not a chemist but I do know that fiberglass, acrylic, or "Vikrell", are made from a variety of components including poly resins and plasticizers which contain phthalic acid or phthalic esters which phthalates are derived from as well as BPAs. The US is following the lead of Europe and Canada and phthalates are being phased out of use in consumer products while BPAs have been banned outright from specific consumer products with likely more to come.

Risk of leaching
It is difficult to say if there is any potential leaching risk from these materials which can be directly linked to health risks with bathtub use.

From a purely structural standpoint, the gelcoat surface of tubs and shower surrounds are highly non-porous (acrylic more so than fiberglass or Vikrell) which should effectively seal in the chemicals of concern.

That said, improper use or maintenance of the tub or shower surround along with prolonged exposure to the sun can degrade the surface layer the tub/shower potentially releasing the phthalates or BPAs.
With respect to the gelcoat itself, this material is designed to be UV resistant and is relatively inert once cured so again leaching should be minimal but the fact is that it too is made from epoxy or polyester resin which may contain phthalates or BPAs.
Making a decision
In conclusion, it is difficult to say definitively that any one material is safer than another.

I can say that acrylic is more durable than fiberglass or Vikrell and that enamel is more durable than acrylic.
There are many factors that go into a product decision selection.
Heath risks appear to be your primary criteria.
When making a product decision, also consider the cost, the manufacturing process (does it release pollutants into the atmosphere), the lifecycle of a product as well as its carbon footprint.

Good luck!