Is it crass to acknowledge a colleague that passed away in my thesis? A PhD student in our school recently passed away unexpectedly, to the shock and  grief of a large number of research students and academics, including me. 

I had little to do with him on a daily basis, and he had little to nothing to do with the content of the thesis, but nonetheless it occurs to me to make a mention of his passing in the acknowledgements of my own (Honours) thesis. 

Is this appropriate, or could it come off as disrespectful?
I certainly don't think it's "crass", and I have a hard time seeing who could be disrespected.  In general, you can acknowledge whomever you want in a thesis and the only crass thing would be to say something negative about them.

However, there is possibly a bit of room for misunderstanding here, because the ostensible purpose of the acknowledgments is to recognize people who helped you out in some way.  Based on what you write -- you were not close, and he did not help on your thesis -- it doesn't make sense to thank this person in the acknowledgements.

I might instead suggest going for a dedication or commemoration.  Some ways of wording this are given here.  You could either end the acknowledgments with a dedication, probably in its own separate paragraph (and you can dedicate the thesis to more than one person, if you like), or you could include the dedication on its own page separately in the thesis, e.g. "For X", "In memory of X (19xx - 20xx)", etc.  

Speaking personally, I like the look of the latter, and I find it to be the opposite of crass to take time out to remember the departed, whether they had a special relationship with you or not.  You are doing your part to make sure that your fellow student will not be completely forgotten for some time to come.  Good for you.