If Shiftry uses "Feint Attack" against a Pokémon that successfully used "Agility" the previous turn, would Agility prevent the Feint Attack or not?
No, the Feint Attack ignores any effects on the Defending Pokémon, including Agility, Wonder Guard, etc.
Source: PUI Rules Team (2004-01-08)

Relevant cards

Note: All applicable cards may not be listed below.
BW2_65
HGSS3_25
PL3_1
EX2_22