Collocations for insensitive - adj.

appear, be, seem, sound
It may sound insensitive, but I don't understand why he's so upset.

become, grow
make sb
think sb
I don't want to be thought insensitive, but I do think we should go ahead despite the accident.

extremely, fairly, very, etc.
highly, incredibly, remarkably
crassly (BrE), grossly (esp. BrE)
totally
a little, slightly, etc.
culturally, racially (esp. AmE)
The decision to serve pork was culturally insensitive.

to
Years of abuse had made him insensitive to others' suffering.

be
remain
make sth/sb, render sth/sb
The device renders the system insensitive to vibration.

extremely, fairly, very, etc.
completely, totally
almost
largely
relatively
Its physical properties are relatively insensitive to pressure changes.

to
The machine is relatively insensitive to changes in the atmosphere.

Insensitive is used with these nouns:
handling, jerk