Rope as strong as 3/16" steel rope?
If low stretch is your objective, a good choice is Spectra™ brand material. It is frequently used with an over-braid cover material to reduce abrasion and contact damage. Spectra™ is used inside support lines for paraglider canopies, as a bit of stretch creates inaccurate lofting of the canopy and control complications. That Spectra™ is typically 1 mm in diameter with an extremely high breaking strength.

You can find 3/16" diameter Spectra™ online and in many local marine or climbing shops. It comes in various colors of over-braid, allowing for better visibility than the natural (whitish) color of the raw material.

The level of stretch is minimal and once tensioned, is likely to stay taut. It is not affected by moisture, but can be damaged by sunlight and UV and may change tension slightly with extreme temperature changes.

As shown on one web site, the breaking strength of 3/16" double braided Spectra™ is 1956 pounds/884 kilograms, certainly strong enough to contain unruly crowds.

It is also relatively attractive if your color selection is done carefully.