[Jackie07]

This 2002 article about a controlled study asserts it's safe to use the hair dye:

Eur J Cancer. 2002 Aug;38(12):1647-52.
Use of hair colouring products and breast cancer risk: a case-control study in Connecticut.

Zheng T, Holford TR, Mayne ST, Owens PH, Boyle P, Zhang B, Zhang YW, Zahm SH.
Yale School of Public Health, 60 College Street, New Haven, CT 06520, USA. tongzhang.zheng@yale.edu
Abstract

This case-control study was designed to test the hypothesis that the risk of breast cancer varies by type and colour of the hair colouring products used. A total of 608 cases and 609 controls were included in the study. We found no increased risk associated with the overall use of hair dye products or exclusive use of permanent or temporary types of hair dye products. Among those who reported to have exclusively used semi-permanent types of hair colouring products, some of the ORs were elevated. However, none of the ORs related to age at first use, duration of use, total number of applications, and years since first use, was statistically significant. There was also no increased risk of breast cancer associated with exclusive use of dark or light hair colouring products, or use of mixed types or colours of hair dye products. We also found no increased risk of breast cancer associated with hair dye use based on an individual's reason for using a hair colouring product, such as to cover grey or to change natural hair colour. These data suggest that the use of hair colouring products does not have a major impact on the risk of breast cancer.