No not normal behavior so you must have some customizations in place or displaying the widget within an area such as ‘sidebar-me’ within sidebar.php that is wrapped in an if( is_user_logged_in()) conditional as an example only, as I would have thought it unlikely you were rendering the widget there as it’s a hardcoded section not widgitised.
You’ll need to read through your files carefully and determine where and how the area your widget is rendering in is working.
I have done quite a bit of editing on my sidebar, but I *think* all of my if conditionals are in order. Here’s my sidebar.php:
http://pastebin.com/C7j10rmp
FWIW, I had this same issue when I stuck widgets in a widgetized area of a custom page template. I have a search and 2 text widgets in a left hand sidebar that display just fine to logged out users. Going to go try sticking the members widget there to confirm.
I also have a conditional on my custom index page template to display some stuff to logged out users only. It works as intended, but could I have not close that correctly or something? Here’s that code:
http://pastebin.com/KYCEvDwq
ETA: just checked, and this widget will not display in my left sidebar either! Must be an issue specific to this one widget, because the others in that area are displaying just fine, whether I’m logged in or out…
ETAA: Here is the portion of my bp-core-widgets.php that pertains to this widget. Can’t remember if I’ve done anything to it other than changing the widget display title:
http://pastebin.com/ntEmPW8J
What other plugins do you have running that might affect things like members or profile displays, pseudo privacy type plugins?
Adminimize (though I thought this only affected admin panel screens) and Capability Manager are the only things I have running that would mess with any of that sort of thing, I think.
Hmmm…I just checked, and it seems like I am able to see this page when logged out:
http://www.riotcart.com/community/members
I also tried another members widget, and it didn’t want to work either 
Oh well, found this:
https://wordpress.org/extend/plugins/hts-display-active-members/
It displays for ALL visitors, and I kinda like the concept a bit better than the original widget anyway 
