JSFiddle - React, Tailwind, and code Playground

HTML

<div class="container">
    <div class="block">
        Как<br>
        реализовать<br>
        адаптивное<br>
        размытие<br>
        фона<br>
        (responsive blur)?
    </div>
</div>

CSS

html,
body {
    height: 100%;
}
body {
    margin: 0;
}
.container {
    position: relative;
    height: 100%;
    background-image: url(http://www.hdwallpaperspics.com/wp-content/uploads/2013/01/Abstract-18.jpg);
    background-size: cover;
}
.block {
    position: absolute;
    top: 0;
    left: 0;
    right: 0;
    bottom: 0;
    margin: auto;
    width: 200px;
    height: 200px;
    font-family: arial, sans-serif;
    font-size: 24px;
    line-height: 32px;
    text-align: center;
    color: #fff;
    background-color: rgba(255, 255, 255, .5);
    box-shadow: 0 0 2px #000;
    filter: url('data:image/svg+xml;base64,PD94bWwgdmVyc2lvbj0iMS4wIiBzdGFuZGFsb25lPSJubyI/Pg0KPHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB2ZXJzaW9uPSIxLjEiDQp4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciDQp4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayI+DQogIDxkZWZzPg0KICAgIDxmaWx0ZXIgaWQ9ImJsdXIiPg0KICAgICAgPGZlR2F1c3NpYW5CbHVyIGluPSJTb3VyY2VHcmFwaGljIiBzdGREZXZpYXRpb249IjIgMiIgLz4NCiAgICA8L2ZpbHRlcj4NCiAgPC9kZWZzPg0KPC9zdmc+DQo=');
   -webkit-filter: blur(2px);
}