Generally I prefer newspaper or cardboard covered with raw wood chips straight out of a tree care co's chipper or aged a bit. Landscape fabric is also a tool I use, but it can be a PIA- for a couple of reasons- none of them pertaining to health issues.

Fabrics need to be covered with mulch and only the woven kind has enough uv resistance to survive more than a short while unprotected from the sun. Even the woven kind tends to shed rain water if it's not covered, although if you make a concave mound or well underneath it it won't do this.

When I use fabric under fruit trees I cover it with woodchips or horse stable waste and lift it carefully every year- scraping away what's left of last years mulch- otherwise it gets imbedded with weeds and/or roots and becomes permanent junk underneath the tree. It also stops being a weed barrier altogether. Spun fabric will wear out after a 3 years or so depending on its thickness.

Woven fabric has clear threads of plastic through it and they start to come loose when you cut it- what you have is probably spun as it's more common.