Problem:

I'd like to have a way to change the Loop style from the front end. Many websites I've visited have something like this to change the style from grid to list to table etc...

Solution:

There isn't such kind of built-in feature within Toolset Views/Blocks plugin, you might consider to create two views, but display them in different style(grid and list), then use custom JS codes to toggle to different view, for example:

Relevant Documentation:

https://api.jquery.com/toggle/