The sentence should be:
Not that it makes having your house turned upside down and your favourite things stolen any easier to accept.
When we use this structure, with 'not' coming first in the sentence, there is usually some information that has been given in the sentence immediately before eg
After my house was burgled (=robbed), the insurance company paid up for the stolen items the next day. Not that it (=having the money from the insurance company to immediately replace all the stolen items) makes ......
Here, 'not that it makes.' is the same as, 'it does not/doesn't make..', but placing the 'not' first, emphasizes how strongly you feel about this.
Another example would be:
"Oh, she and I went out for a while, but then she dumped me. Now she's dating the captain of the football team. Not that I care."
In this sentence, the person is emphasizing how little he cares that the girl seems to have found herself a much better boyfriend than he is/was...which probably means he is feeling pretty inadequate and second-rate!
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