To execute automatic Xss check, the old MVC used the logic implemented in the System.Web.CrossSiteScriptingValidation class. However this class is not present in ASP.NET CORE 1. So, to reuse it I copied its code:
System.Web.CrossSiteScriptingValidation class
// <copyright file="CrossSiteScriptingValidation.cs" company="Microsoft">
//     Copyright (c) Microsoft Corporation.  All rights reserved.
// </copyright>
public static class CrossSiteScriptingValidation
{
    private static readonly char[] StartingChars = { '<', '&' };
    #region Public methods
    // Only accepts http: and https: protocols, and protocolless urls.
    // Used by web parts to validate import and editor input on Url properties. 
    // Review: is there a way to escape colon that will still be recognized by IE?
    // %3a does not work with IE.
    public static bool IsDangerousUrl(string s)
    {
        if (string.IsNullOrEmpty(s))
        {
            return false;
        }
        // Trim the string inside this method, since a Url starting with whitespace
        // is not necessarily dangerous.  This saves the caller from having to pre-trim 
        // the argument as well.
        s = s.Trim();
        var len = s.Length;
        if ((len > 4) &&
            ((s[0] == 'h') || (s[0] == 'H')) &&
            ((s[1] == 't') || (s[1] == 'T')) &&
            ((s[2] == 't') || (s[2] == 'T')) &&
            ((s[3] == 'p') || (s[3] == 'P')))
        {
            if ((s[4] == ':') || ((len > 5) && ((s[4] == 's') || (s[4] == 'S')) && (s[5] == ':')))
            {
                return false;
            }
        }
        var colonPosition = s.IndexOf(':');
        return colonPosition != -1;
    }
    public static bool IsValidJavascriptId(string id)
    {
        return (string.IsNullOrEmpty(id) || System.CodeDom.Compiler.CodeGenerator.IsValidLanguageIndependentIdentifier(id));
    }
    public static bool IsDangerousString(string s, out int matchIndex)
    {
        //bool inComment = false;
        matchIndex = 0;
        for (var i = 0; ;)
        {
            // Look for the start of one of our patterns 
            var n = s.IndexOfAny(StartingChars, i);
            // If not found, the string is safe
            if (n < 0) return false;
            // If it's the last char, it's safe 
            if (n == s.Length - 1) return false;
            matchIndex = n;
            switch (s[n])
            {
                case '<':
                    // If the < is followed by a letter or '!', it's unsafe (looks like a tag or HTML comment)
                    if (IsAtoZ(s[n + 1]) || s[n + 1] == '!' || s[n + 1] == '/' || s[n + 1] == '?') return true;
                    break;
                case '&':
                    // If the & is followed by a #, it's unsafe (e.g. S) 
                    if (s[n + 1] == '#') return true;
                    break;
            }
            // Continue searching
            i = n + 1;
        }
    }
    #endregion
    #region Private methods
    private static bool IsAtoZ(char c)
    {
        return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');
    }
    #endregion
}
Than,in order to use the above class for all requests, I created a Middleware that use CrossSiteScriptingValidation class:
AntiXssMiddleware
public class AntiXssMiddleware
{
    private readonly RequestDelegate _next;
    private readonly AntiXssMiddlewareOptions _options;
    public AntiXssMiddleware(RequestDelegate next, AntiXssMiddlewareOptions options)
    {
        if (next == null)
        {
            throw new ArgumentNullException(nameof(next));
        }
        _next = next;
        _options = options;
    }       
    public async Task Invoke(HttpContext context)
    {
        // Check XSS in URL
        if (!string.IsNullOrWhiteSpace(context.Request.Path.Value))
        {
            var url = context.Request.Path.Value;
            int matchIndex;
            if (CrossSiteScriptingValidation.IsDangerousString(url, out matchIndex))
            {
                if (_options.ThrowExceptionIfRequestContainsCrossSiteScripting)
                {
                    throw new CrossSiteScriptingException(_options.ErrorMessage);
                }
                context.Response.Clear();
                await context.Response.WriteAsync(_options.ErrorMessage);
                return;
            }
        }
        // Check XSS in query string
        if (!string.IsNullOrWhiteSpace(context.Request.QueryString.Value))
        {
            var queryString = WebUtility.UrlDecode(context.Request.QueryString.Value);
            int matchIndex;
            if (CrossSiteScriptingValidation.IsDangerousString(queryString, out matchIndex))
            {
                if (_options.ThrowExceptionIfRequestContainsCrossSiteScripting)
                {
                    throw new CrossSiteScriptingException(_options.ErrorMessage);
                }
                context.Response.Clear();
                await context.Response.WriteAsync(_options.ErrorMessage);
                return;
            }
        }
        // Check XSS in request content
        var originalBody = context.Request.Body;
        try
        {                
            var content = await ReadRequestBody(context);
            int matchIndex;
            if (CrossSiteScriptingValidation.IsDangerousString(content, out matchIndex))
            {
                if (_options.ThrowExceptionIfRequestContainsCrossSiteScripting)
                {
                    throw new CrossSiteScriptingException(_options.ErrorMessage);
                }
                context.Response.Clear();
                await context.Response.WriteAsync(_options.ErrorMessage);
                return;
            }
            await _next(context);
        }
        finally
        {
            context.Request.Body = originalBody;
        }            
    }
    private static async Task<string> ReadRequestBody(HttpContext context)
    {
        var buffer = new MemoryStream();
        await context.Request.Body.CopyToAsync(buffer);
        context.Request.Body = buffer;
        buffer.Position = 0;
        var encoding = Encoding.UTF8;
        var contentType = context.Request.GetTypedHeaders().ContentType;
        if (contentType?.Charset != null) encoding = Encoding.GetEncoding(contentType.Charset);
        var requestContent = await new StreamReader(buffer, encoding).ReadToEndAsync();
        context.Request.Body.Position = 0;
        return requestContent;
    }
}