Hi
I guess there is an argument to non-index them because one want to have the search engine to focus fully on the parent product. Is that a valid assumption?
More of a choice than an assumption. I'd say it depends a lot on how different the child are from the parent product, in which way they vary. Another factor is how large the site is and how many of these product/child product you have. If a few hundreds or even a few thousands in total, that's likely not a major issue?
And then, to follow or not-follow?
I don't see any reason to nofollow links on this child product pages, I guess they are the same product page format as the rest and therefore the links are likely the same as everywhere? or which page are thinking on putting nofollow on? parent or child?
Note however, that if you noindex a page, Google (not others) have stated that even if there's a follow tag, they'll consider the page a nofollow after a while (a few months?).
Lastly, I'm happy to give an opinion here but I'm definitely not an SEO consultant, who would have to look at your site, its metrics, analytics, markets, location and many other things before being able to answer without just giving very broad, general answers...
Best regards
Yannick Gaultier
weeblr.com / @weeblr