Android webview dropdown menu does not work on Android 4.x devices

I have a problem with one of my WebView on Android 4.x devices.

Android app has a Tabhost which contains Fragments. One of the fragments contains a webview. The displayed page has a dropdown menu like this:

<select id="mySelect" name="mySelect">
    <option value="1">Testname 1</option>
    <option value="2">Testname 2</option>
    <option value="3">Testname 3</option>
</select>

Now when I open my app with a Galaxy S3 with Android 4.1.1 (or any other Android device I could get my hands on) I can select "Testname 1", then "Testname 2" and so on.

On the Galaxy Nexus (confirmed on different devices running Android 4.1.1, 4.1.2 and 4.2) when I try to select something the UI just blocks. After I switch to another tab and back to the webview tab suddenly the UI finally changes to the previously selected item.

Any idea what is causing this or how I can fix this for the Galaxy Nexus?

Important update: I could track this down to the Tabhost. When the webview is in the tabhost it does not work, when it is not it works. This might be related to this issue.