not logged in users can't submit form

I embedded a Mailchimp newsletter registration using the mailchimp-plugin, which works just fine for logged in users and also on other websites of mine. But on this page, users who are not logged in, can't click the submit button hof the form. It just has no effect and no error message appears. Nothing is happening.

EDIT: Could the problem be the fact, that there are two forms on the page, when the user isn't logged in and mailchimp can't figure out which input field are the right ones?! The weird thing is, that it works fine, if I use the option "convert text inputs to textarea", of the browser plugin 'web developer'!

Here is my form:

    form class="snp-subscribeform snp_subscribeform layout_form cr_form cr_font" method="post"
  script type="text/javascript"
    (function() {
      if (!window.mc4wp) {
        window.mc4wp = {
          listeners: [],
          forms: {
            on: function(event, callback) {
              window.mc4wp.listeners.push({
                event: event,
                callback: callback
              });
            }
          }
        }
      }
    })();
  /script
  div class="mc4wp-form-fields"
    div rel="text" class="cr_ipe_item ui-sortable musthave footer-newsletter_firstname" input type="text" name="FNAME" placeholder="Firstname*" required=""/div
    div rel="text" class="cr_ipe_item ui-sortable musthave footer-newsletter_lastname" input type="text" name="LNAME" placeholder="Lastname*" required=""/div
    div rel="email" class="cr_ipe_item ui-sortable musthave footer-newsletter_email" input type="email" name="EMAIL" placeholder="E-Mail*" required=""/divinput type="hidden" name="INTERESTS[57aa0ce9f6]" value="ccbb36e6a3"
    div rel="button" class="bld-el-cont bld-el-button cr_ipe_item ui-sortable submit_container" input type="submit" class="bld-el cr_button" value="Register" name="mc_newsletter_submit"/div
    div style="display: none;"input type="text" name="_mc4wp_honeypot" value="" tabindex="-1" autocomplete="off"/divinput type="hidden" name="_mc4wp_timestamp" value="1502116875"input type="hidden" name="_mc4wp_form_id" value="7342"input type="hidden" name="_mc4wp_form_element_id"
      value="mc4wp-form-1"/div
  div class="mc4wp-response"/div

List of involved plugins:

• hide my wp (premium)
• All In One WP Security
• buddypress
• Contact Form 7
• iThemes Security
• MailChimp für WordPress
• Plugin Organizer
• W3 Total Cache
• WP-SpamShield
• WP-Sweep

I guess some of these plugins is blocking a script, redirect or something. I renamed/deactivated already the Plugins All In One WP Security, iThemes Security, W3 Total Cache, WP-SpamShield, WP-Sweep, and hide my wp, but nothing changed. I would be appreciated for your help!