mdb-select seems to be still buggy in Version 4.5 (testet with IE11, Edge and Firefox).

1. Dropdown list disappears when klicking scrollbar in IE11, OK in Edge and Firefox
2. IE11 shows blinking cursor when opening the dropdown list, OK in Edge and Firefo
   Can be reproduced by opening https://mdbootstrap.com/javascript/material-select with IE11.
3. Selected item not marked as active when opening the dropdown list the first time. After selecting an item from the list and opening the list again, it is marked as active. Appears in IE11, Edge and Firefox.

To reproduce, I created a simple ASPX-Webform like this:

<main>
 <form id="form1" runat="server" class="mx-2 my-2">
  <div>
   <select id="testSelect" class="mdb-select"></select>
  </div>
 </form>
</main>
.
(scripts references for jquery-3.2.1-, popper-, bootstrap-, mdb-min.js)
.
<script type="text/javascript">
   $(function () {
      let objSelect = $("#testSelect");
      if (objSelect.length > 0) {
         objSelect.material_select('destroy');
         let s = "";
         for (let i = 1; i <= 30; i++) {
            s += "<option";
            if (i === 15) {
               s += " selected=\"selected\"";
            };
            s += " value=\"" + i.toString() + "\">" + "test " + i.toString() + "</option>"
         };
         objSelect.html(s);
      };
      objSelect.material_select();
   });
</script>