Assuming that you are accessing a particular url on the webview in react native, then in the url, you can use the following tricks:
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 
 <meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<div style="font-size:80%;padding-left:10px;padding-right:10px;">
<!DOCTYPE html>
<html>
<head>
  <script>
    function absorbEvent_(event) {
      var e = event || window.event;
      e.preventDefault && e.preventDefault();
      e.stopPropagation && e.stopPropagation();
      e.cancelBubble = true;
      e.returnValue = false;
      return false;
    }
    function preventLongPressMenu(node) {
      node.ontouchstart = absorbEvent_;
      node.ontouchmove = absorbEvent_;
      node.ontouchend = absorbEvent_;
      node.ontouchcancel = absorbEvent_;
    }
    function init() {
      preventLongPressMenu(document.getElementByTagName('body img'));
    }
  </script>
  <style>
    *:not(input):not(textarea) {
    -webkit-user-select: none; /* disable selection/Copy of UIWebView */
        -webkit-touch-callout: none; /* disable the IOS popup when long-press on a link */
    }
  </style>
</head>
<body onload="init()"  >
TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>TEST<br>
</body>
The above will disable text selection, but it allows other functions such as "click". (it works in both iOS and android devices)
Enjoy...