You'll need to create a custom route otherwise Umbraco will intercept the request. Try adding this to your solution:

using System;
using System.Configuration;
using System.Web.Routing;
using Umbraco.Web;
using Umbraco.Web.Mvc;

namespace MyNamespace
{
    public class RouteConfig
    {
        public static void RegisterRoutes(RouteCollection routes)
        {
            routes.MapUmbracoRoute(
                "logOut",
                "LogOut",
                new
                {
                    controller = "Membership",
                    action = "MvcMemberLogout"
                },
                new UmbracoVirtualNodeByIdRouteHandler(1050); // set this to an actual node ID e.g. your homepage
        }
    }
}

Then you should be able to hit /logout.

Remember to call RouteConfig.RegisterRoutes:

public class Startup : ApplicationEventHandler
{
    protected override void ApplicationStarted(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
    {
        base.ApplicationStarted(umbracoApplication, applicationContext);

        RouteConfig.RegisterRoutes(RouteTable.Routes);
    }
}

There's documentation on custom routes here:

https://our.umbraco.org/documentation/reference/routing/custom-routes