Strider is not unique in this regard when it comes to the Nazgul...tho perhaps
of all "mortals" the most consistent. Other examples from later on in the
series (sorry if i'm getting too far ahead of myself) include Beregond in Minas
Tirith, who overcomes the terror of the Nazgul to observe their chase of
Faramir (who himself seems impervious to their terror, tho ultimately he may
become a victim of it). And of course there is also Eowyn, and Merry for
that matter.
We'll leave Eowyn and her mental state for a more appropriate time...but in
general it seems that other emotions such as compassion or "love" may in
certain instances be powerful enough to overcome the terror of the Nazgul.
Particularly so in those such as the Dunedain (or even hobbits) who are
somewhat "genetically" more resisitant (tho I'm sure Tolkein would never put it
in those
terms!).