The only way I know of to do this in InDesign is to remove the stroke before doing your alignment, and then add it back afterward.
The two programs don't work the same because 1) they were developed at different times by different teams and 2) their base purposes are not the same.
InDesign is primarily for page layout, with some basic vector drawing tools built in; Illustrator is a vector drawing program with some basic page layout tools built in.
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I don't think there is any way to change how Indesign creates the bounding area of a selection. But for your task at hand, here is a workaround to insure the objects with centered strokes are aligned: Use the Distribute Spacing and set the Spacing value equal to negative value of the stroke.
Your suggestion works, but at the end of the ay it's a clumsy work-around. I'm designing forms and have hundreds of boxes to position. Being able to snap them to my guides without the line thicknesses doubling up would have saved me a lot of work.
Your reasons for the two applications working differently are understood, but I disagree that they are good reasons for making what is essentially exactly the same thing work so differently. In my opinion, Illustrator has it right (and it can be made to work like indesign when it's needed), and Indesign is broken.
I've filed a "feature request" but I think it really ought to be a bug report.
I had a project where I needed centered strokes. What I did was, that I created all frames with an object style where the stroke was 0. So it is a simple easy task to align all frames. At the end I changed the strokes in the Object Style definition. Sie every frame is now as it should be.
Go ahead and file at a bug report then. You know what happen to it?
It will be marked “as designed” and that will be end of it.
Just because you don’t like a particular behavior (and I can see why you don’t) doesn’t make it a bug.
It may not be a bug, but it's incredibly frustrating when common features (like strokes) behave so differently in two apps from the same company, that are marketed as cooperative parts of a suite no less.
When the InDesign development team were working on the code for stroke behavior, you'd think they might have said "hey, those Illustrator folks have already done this. Let's incorporate that into InDesign!"
Been using AI since, well, forever, and InDesign since v1.0, so I'm long-accustomed to the inconsistencies and working around them. Doesn't mean I like it, tho...
(And don't even get me started on the complete travesty that is "vector" data in a PDF generated from Photoshop... quotes very intentional!)