There are a number of people who have found using sandals or water shoes to be highly effective. They provide excellent ventilation for your feet, and are ideal when you are in wet conditions because they don’t hold water against your feet. The downsides of using sandals or water shoes are that your feet get really dirty and most sandals don’t protect your toes.
I really like Luna Venado Sandals for street running and walking on city streets. I have used them in the back country, but they don’t have a lot of traction. For me, the Luna Oso Flaco Sandals are the best all around sandal. Enough ground feel that they don’t feel “dead” when I run in them, but enough traction to use in the back country. Bedrock Cairn 3D Sandals are the best pure hiking sandals I have found: grippy on the top and bottom but a bit dead feeling.
Keen makes a wide range of shoe including sandal like shoes with a toe guard. Many people seem to love the durable but heavy Chaco Sandals, which are a bit like a hiking boot sole with sandal straps. I don’t use them because they have a very pronounced arch support ridge which hits me in exactly the wrong place. Teva and Xero Shoes make a wide variety of sandals which can be used for a wide variety of activities. There are a number of companies that made minimalist versions of Huaraches running sandals such as Earthrunners, Luna Sandals, and Unshoes. Mayflyultralight made an ultralight sandal which doesn’t have a strap between your toes. There was a nice set of mini reviews of minimalist running sandals on reddit.