Hi @VictorPorton, thanks for taking the time to report this!
Unfortunately this report lacks some information. If you have time and can still reproduce the problem, please add a more complete description to this report as "does not work" can mean a lot of things.
Ideally, exact and clear steps to reproduce should allow any other person to follow these steps (without having to interpret those steps, e.g. which exact versions of MediaWiki and the extensions were used) and see the same results. Problems that others can reliably reproduce can get fixed faster. Thanks!

I've installed MediaWiki 1.26.2 with AJAX Poll 1.88.0 20140330 and MobileFrontend 1.0.0.

In the desktop (default) version of wiki voting works.

But when I click "Mobile view" in the footer and so show mobile version in my browser (Firefox 45.0.2 for Linux) voting ceases to work: When I click a question, the radio button becomes selected, but nothing happens (no "Your vote has been added." message and no change in voting results (as I can see switching back to desktop version)).

Also there are no "console" (JavaScript) error messages.

I will attach a screenshot (which by the way shows internal information "poll ID", which should not be visible).

My settings are below:

require_once "$IP/extensions/AJAXPoll/AJAXPoll.php";

$wgGroupPermissions['*']['ajaxpoll-vote'] = true;
$wgGroupPermissions['*']['ajaxpoll-view-results'] = true;
$wgGroupPermissions['*']['ajaxpoll-view-results-before-vote'] = true;

require_once "$IP/extensions/MobileFrontend/MobileFrontend.php";

Change 445777 had a related patch set uploaded (by Jack Phoenix; owner: Jack Phoenix):
[mediawiki/extensions/AJAXPoll@master] Load AJAXPoll assets for MobileFrontend so that MF users can also vote in polls (if the wiki is configured so) + polls will look nicer

https://gerrit.wikimedia.org/r/445777

Change 445777 merged by jenkins-bot:
[mediawiki/extensions/AJAXPoll@master] Load AJAXPoll assets for MobileFrontend so that MF users can also vote in polls (if the wiki is configured so) + polls will look nicer

https://gerrit.wikimedia.org/r/445777