It will probably not be possible to determine whether it is safe or not.
I had this recently on a well known accommodation booking site, I looked at the assurance offered by the service provider that the site was using and it was not particularly compelling so I did not submit anything.
I would not submit a full image of any official documentation to any site without some form of independent corroboration that security claims can be trusted.
However it depends what is on your ID card as to whether you should be concerned or not, I would say that the place your were born is not something that you would want to risk being compromised and it is generally not readily available on the Internet for most people, but on the flip side many people will submit it in a security question without giving it a second thought.
Other things I would not be comfortable providing...document reference number and signature along with anything else specific to the ID.
From what I have observed there are specific aspects of the ID that will be checked, for example a signature can probably be edited out of a scan without impacting the ID check, but a lack of document ID is probably going to cause it to fail.
When making your decision put things into perspective about the way you normally treat your personal data (i.e. break it down into a list: name, address etc) and decide first whether you would submit all of the information in a website registration form - it may be that you have already provided the site much of your information!
Having said all that, personally I would advise against it...once information has been leaked you cannot get it back.