Is a bone marrow transplant limited by sex?
Short answer: Yes. Because in almost all cases of organ transplant, the organ recipient will be administered immunosuppressive drugs.

There is some literature on the effect of sex on the outcomes. I have included two hints here.

from: http://www.nature.com/bmt/journal/v35/n6/full/1704861a.html

The impact of the donor gender on outcome in HLA-identical sibling donor hematopoietic stem cell transplantation for multiple myeloma was studied in a retrospective registry study of 1312 patients (476 male to male (M → M); 334 female to male (F → M); 258 male to female (M → F); 244 female to female (F → F) reported to the European Group for Blood and Marrow Transplantation (EBMT). The best overall survival (OS) from the time of transplantation was found in F → F (median 41 months) with no significant difference between other groups (median 25 months in M → M, 18 months in F → M, 19 months in M → F) despite a significantly higher nonrelapse mortality in F → M. This was due to a significantly lower relapse rate (REL) in F → M compared to all other groups. Before 1994, OS was poorer in F → M than in M → M, which improved to similarity from 1994 onwards (median 29 months in M → M and 25 months in F → M). The reduced REL contributed to this improvement in F → M indicting a sex-specific graft vs myeloma effect. Therefore, a female donor is as good as a male one for male patients, while for female patients gender disparity is a negative factor for outcome.

from: https://www.broadinstitute.org/news/1386

"It's been clear for some time that bone marrow transplants involving a female donor and a male patient pose a higher risk of GVHD," said Bradner. "This ‘sex mismatch' arises from genes that are carried on the male-specific Y chromosome and are therefore present in males but not in females..."