There are laws in place to prevent this from happening, look up the Magnuson Moss Act. In a nutshell, it prevents dealers/companies from refusing to offer warranty simply because modifications have been made to the vehicle... among other things. They would need to provide evidence without any reasonable doubt that the specific modification you made was directly responsible for the warranty item in question. So, that is possible for some items when talking about larger tires... but not many, and it certainly doesn't void your warranty entirely.
As some have mentioned, often dealers simply don't know about this or refuse to touch the vehicle because they don't know what is allowed or not allowed. I agree that sometimes it can be easier to just find a new dealer, but at the end of the day you do have the Magnuson Moss act to fall back on.
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