Are PHP short tags acceptable to use?
They're not recommended because it's a PITA if you ever have to move your code to a server where it's not supported (and you can't enable it). As you say, lots of shared hosts do support shorttags but "lots" isn't all of them. If you want to share your scripts, it's best to use the full syntax.
I agree that <? and <?= are easier on programmers than <?php and <?php echo but it is possible to do a bulk find-and-replace as long as you use the same form each time (and don't chuck in spaces (eg: <? php or <? =)
I don't buy readability as a reason at all. Most serious developers have the option of syntax highlighting available to them.
As ThiefMaster mentions in the comments, as of PHP 5.4, <?= ... ?> tags are supported everywhere, regardless of shorttags settings. This should mean they're safe to use in portable code but that does mean there's then a dependency on PHP 5.4+. If you want to support pre-5.4 and can't guarantee shorttags, you'll still need to use <?php echo ... ?>.
Also, you need to know that ASP tags <% , %> , <%= , and script tag are removed from PHP 7. So if you would like to support long-term portable code and would like switching to the most modern tools consider changing that parts of code.
I'm too fond of <?=$whatever?> to let it go. Never had a problem with it. I'll wait until it bites me in the ass. In all seriousness, 85% of (my) clients have access to php.ini in the rare occasion they are turned off. The other 15% use mainstream hosting providers, and virtually all of them have them enabled. I love 'em.
Starting with PHP 5.4, the echo shortcut is a separate issue from short tags, as the echo shortcut will always be enabled. It's a fact now:
So the echo shortcut itself (<?=) is safe to use now.