Give somebody the freedom to make mistakes or give somebody the space to make mistakes.
These are often used in the context of management and education. It's a bit nicer than talking about hanging (or shooting oneself in the foot).
Amy Rees Anderson wrote in Forbes: "As a business leader, I found that one of the scariest things to do was to give your people the freedom to make mistakes." (Amy Rees Anderson, "Good Employees Make Mistakes. Great Leaders Allow Them To.", Forbes, April 17, 2013)
Graeme Richardson wrote something similar in The Guardian: "But universities, it seems to me, are a good place for making mistakes; and the freedom which is a university's soul includes the freedom to make mistakes." (Graeme Richardson, "A university's soul is the freedom to make mistakes", The Guardian, Oct 22, 2010)
Jack Kornfield claims Gandhi said "Freedom is not worth having if it does not include the freedom to make mistakes." I don't know if Gandhi said this, but it's still a good maxim. (Jack Kornfield, "Freedom to make mistakes", Jack Kornfield blog)
These are neutral expressions, a lot more positive than "give someone the rope to hang themselves", which recognise that sometimes making mistakes are the best way to learn. If you say "give someone the rope to hang themselves" or similar expressions about "shooting themselves in the foot" you appear to expect the person to do something stupid, or even to gloat about it.