Is it ever appropriate to "politicize" a death?

The death of Mollie Tibbetts at the hand of an illegal immigrant has naturally started a conversation about immigration reform. Some of Tibbetts’ family members have spoken out against the politicization of her death.

A similar type of thing happens after a mass shooting: the conversation immediately turns to gun control.

Both the left and the right are guilty of this. The left will leap to gun control and the right will leap to immigration reform. Both sides hypocritical accuse the other of politicizing death but do it themselves. This isn’t about left vs. right.

Instead what I want to know is when it is appropriate to talk about politics after a tragedy? Is there a way to talk about political solutions to the societal problems that caused these deaths without being callous?