Hello,
I am wondering how badly seeds could be hybridized,
https://sheffields.com/products/view/894
" The 2019 lot from Louisiana could be hybridized with M. alba, etc."
Hunting for real North-American Morus Rubra 
I have few plants (not seeds) from different vendors but I believe they rely on fruit colour in description…
I think you are right for concern. Your best bet is perhaps to go out somewhere away from any civilization and collecting your own. Red Mulberry can be found on the banks of rivers. Some respectable “forestry” nurseries have quit offering Red Mulberry seedlings because they have realized they are not pure.
We have some fruiting trees in local park, but those are mostly hybrids… there is even white-fruiting mulberry at High Park, Toronto.
According to this publication (from 2015), "The total known Canadian population of Red Mulberry includes 217 individuals, only 105 of which are considered mature (over 10 cm in diameter at breast height), representing a 6.3% decline in the number of mature individuals since the last assessment, despite ongoing discovery of new trees at some sites.
http://publications.gc.ca/collections/collection_2016/eccc/CW69-14-142-2015-eng.pdf
SO, I am going for a hunt there are few websites (including government) where I need to submit report if I find any…
I haven’t spotted that publication before. They even have a map! Sorry, I forgot you live in Canada, so finding a rubra in the wild is like looking for Bigfoot. I had tried to contact Burgess a couple years ago after reading his earlier study (Asymmetrical introgression between two Morus species (M. alba, M. rubra) that differ in abundance. Mol Ecol 14: 3471-3483) but was unsuccessful. Good luck.
One tree is growing at The Arboretum of University of Guelph, not so far; I may visit them sometime to see the tree (to study how it looks like and to make photos; not to collect fruit ;))
https://www.uoguelph.ca/arboretum/thingstosee/trees/redmulberry
Detailed list at this page, need to visit Hamilton - 64 trees