if by "dropped in from Illustrator", you mean dragged or pasted, I suggest you don't use that way and use "Import" function instead.
The "import function" is the File > Place command, just in case that is not clear.
Sit back, close your eyes and repeat after me: "there are no blue outlines".
InDesign shows the bounding box and/or outline of objects. That is a good thing -- how else would you be able to see a white object on a white page?
InDesign shows the bounding box and/or outline of objects not "in blue" but in the color of the layer they reside on. That means you can immediately see on what layer an object lies.
InDesign shows outlines around your "Illustrator" artwork, not because it comes from Illustrator but because you pasted it as native InDesign artwork, and so InDesign's rules apply. You should not be doing this in the first place "by default"; for regular artwork you can simply import the AI document.
Finally, if the blue outlines really, really bother you and you cannot imagine what your document would look like without and you don't "want" to place the original file, there are still plenty options left. Go into Preview mode (see? no helpful lines anywhere!), or select "Hide Frame Edges" in the View menu.
Press the W key. W is for “Will someone get rid of these darned blue lines for me?”
I hope you are asking about frame edges..
If that is the case choose View > Extras > Show/Hide Frame Edges.
I know this man is a savior.