If I use Shiftry's "Fan Tornado" attack and my opponent has an Active Pokemon that used its "Swim Freely" attack on their last turn, can I still choose to have them switch their Active Pokemon with a benched Pokemon if they flipped heads for "Swim Freely"
No, the effect of Fan Tornado is targeting the Active Pokemon (not the Benched Pokemon), and therefore is prevented due to the effect of Swim Freely.
Source: Lost Origin FAQ; TPCi Rules Team (2022-09-08)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH11_13
SWSH11_13
SWSH11_34
SWSH11_34
SWSH11_36
SWSH11_36
SWSH11_41
SWSH11_41