Lots of SIDs around the world have specific mention to the very scenario you describe. For example, Toronto Pearson (YYZ) has a notation in the altitude box for almost every RNAV SID that describes what to do in the case of a tower or departure initiated turn away from the SID profile. In this specific case it is for noise abatement purposes, but as far as I am concerned the controller has the bigger picture, so I go where they tell me to - unless my EGPWS shows red and begins talking to the voices in my head.
As for STARs, Feather44 already mentioned that this can leave us high and fast with some controllers still expecting the airplane to be able to meet all speed and/or altitude restrictions afterwards. The phrase "do your best" often gets chuckles from all the other airplanes on frequencies and grumbling from the airplane it was directed towards.
Feather44, if they say "Climb/Descend via the SID/STAR, cleared direct xxxx" then you are responsible for meeting any previous altitude and/or speed restraints that would normally apply at that waypoint.
If they do not specifically state "Climb/Descend via" and you are cleared to a waypoint, you do not need to meet any previous restriction but you must meet any restriction ahead of you.
This is fairly new here in Canada as we adopt a more ICAO style format, so I've been double checking anyways as a bit of CYA.