Let me shortly explain the reason of such a conflict (for other readers).
Mobile Joomla detects home page by analyzing of global $_GET array that contains parameters from URL (and parameters from parsed SEF URL). In the case of homepage it's either empty, or contains parameters of home menu item only.
But GTranslate plugin pollute this array with a lot of additional parameters (api_key, bing_api_key, cache_time, ssl_verify_peer, auto_detect, auto_detect_user, main_lang, and debug_mode). As a result, MJ cannot detect homepage correctly.
The only solution here is to patch plugins/system/mobilebot.php (because of GTranslade is crypted by ionCube) by adding
And unlikely this patch will be included into official MJ release, so you should apply it after each MJ update.