Broad match negative keyword affect other match types?

Yes. You are in effect preventing your "white cotton dress" keywords from triggering your ads. Negative means "don't show my ads if this keyword is part of the search query".

Can I ask what the purpose was of adding "white" as negative?

the way we're using double quotes here, it can indicate either phrase matching, or just that you're quoting something... to avoid confusion, suggest using a single quote when quoting, and reserve the double quote for indicating phrase match.

if you added 'white' as a broad neg, you added -white

and yes, as others said, with that neg, you'll block all of these positive keywords:
[white cotton dress]
"white cotton dress"
white cotton dress

but...

on the broad 'white cotton dress', you won't block everything.
for example, synonyms to white, may come thru, like:
ivory cotton dresses
bleached cotton sundress
cotton dresses that match magnolia flowers

you can address those by using modified broad, like:
+white +cotton +dress