For example there is documented cross protection in other viral infections: HSV-1 can interfere with the expression of Human Papillomavirus (HPV-18) genes in cells by reducing the amount of papillomaviral mRNA when they are infected concurrently with HPV and HSV.
HSV-1 and -2 are antigenically similar and therefore they induce cross-reactive immunity. There is no such similarity between HSV and HIV and no cross-reactive immunity. So, HSV infected subjects are not HIV immune
HSV immunity cannot protect against HIV infection. Moreover HSV-infected persons are more susceptible to HIV, probable due to mucosal lesions induced by HSV. There are a few epidemiological studies on this matter.