Elmer’s, the glue company, has introduced a line of “nonhazardous” home repair products, including wood glue, wood filler, flooring and other miscellaneous adhesives, caulk and glazing, spackling compounds, and tile grout.
Their website very conveniently links to the MSDS for each product. Many list no hazardous ingredients, others list limestone and quartz. These are hazardous only as dusts, which wouldn’t be a problem under normal use, but might be cause for protective gear if sanding something on which you had used the product. They are mostly made of an acrylic/latex blend, so they are not at all natural, but much less toxic than other products of this type.
I haven’t personally experienced all of these products, but I did sniff the stainable wood glue and the wood filler, both of which have MSDS with no hazardous ingredients listed. The stainable wood glue was fine, just smelled like white glue. The wood filler had a bit of an odor, but nothing like toxic wood filler.
These are sold at Home Depot, so are widely available and inexpensive.