Which is appropriate?
One of the most significant adversities that (have or has) affected me was …
Which is appropriate?
One of the most significant adversities that (have or has) affected me was …
Both are correct. The difference is very clear, though it generally doesn't strike at once. Think again.
One of the most significant adversities that have affected me was …
(Many adversities affected me, one of them was …)
One of the most significant adversities that has affected me was …
(There were many adversities, one of them that affected me was …)
One of the most significant adversities that affected me was …
is another possibility.
I would say "have", the subject being "things", and then "was", the subject being "one".
Otherwise, "many things" would be connected to nothing and left dangling.