[Vuejs]-How to allow users to access some routes publicly with VueJS Router/SPA

That can be done from your laravel route

Inside your routes>api.php file,

Route::middleware('auth:api')->group(function(){
 // contains the api controllers to be accessed when user is logged in
}

//list of routes to be accessed publicly goes here, e.g.
Route::get('/userworkexperience/{user}', 'ControllerName@method')->name('something.else');

I hope this helps