MRSA can be spread simply by contact. So it is quite easy to spread MRSA around.
In a human colonisation by MRSA is treated with an aquasept skin wash and bactroban nasal cream. Colonisation isn't the same as infection. The organism here is staphlococcus aureus and is a normal skin organism, the only difference is that it is resistant to certain antibiotics, so that if colonisation develops into infection it can be difficult to treat because of this resistance. Hence the concern over MRSA exposure in the immunocompromised as they are more likely to develop infection from colonisation by MRSA and wil also be less capable fighting it off. A diabetic state is recognised as a condition where infections are more easily picked up and hence can be considered an immunocompromised state. There is hence risk of infection from MRSA developing in this case. Particulary if the diabetic in this case has exposed diabetic ulcers which could easily become infected. Colonisation onto a skin surface could easily result in MRSA cellulitis. Your friend should hence avoid direct contact with this cat till the MRSA is cleared. It would be wise to consult a vet to discuss best way to treat MRSA in the cat given the situation not sure where the MRSA is sited in the cat as that has not been mentioned.
Note even if MRSA colonises onto your friend this does not necessarily have any consequences, although it would be desireable to eradicate the MRSA. The colonisation only represents a risk in a difficult to treat infection developing. Obviously the progression of the diabetes and other comorbities is also relevant for instance if she has badly controlled diabetes and complication in the form of peripheral neuropathy and exposed ulcers the risk of infection is much much greater than for instance if she is a simple diet controlled diabetic with no other problems.
I hope this information is useful, feel free to reply for any clarification