So I'm not sure how the anti rejection drugs would affect the male uterus transplant recipient in pregnancy
As you indicate, there are lots of other issues to be researched and resolved before transplant into a male to sustain a viable pregnancy is realistic.
It might be interesting to see the ethical approval in Sweden or other centres when they initiate this.
From the UK paper below, I wouldn't be too surprised if people start using this as an argument for starting hormone treatment in children to bypass some of the anatomical and pelvic issues. My substantial apprehension is that one of the plausible uses of this surgery will be to restore fertility and pregnancy tolerance in transmen who started transition early.
(US) Perceptions and Motivations for Uterus Transplant in Transgender Women :
Question What are the perceptions and motivations of transgender women for uterus transplant?
Findings This survey study of 182 transgender women found that to more than 90% of the respondents indicated that uterus transplant may improve quality of life in transgender women, alleviate dysphoric symptoms, and enhance feelings of femininity.
Meaning This report on the desire and willingness of transgender women to undergo uterus transplant may support the need for further animal and cadaveric model research, which is necessary to assess the feasibility of performing this procedure in transgender women.
jamanetwork.com/journals/jamanetworkopen/fullarticle/2775302
From UK perspective with some discussion of ethics and relevant issues: Uterine transplantation in transgender women
Sexual dimorphism arises predominantly due to the outcome of gender‐determined autosomal genes, which are regulated by sex‐specific hormones and influenced by hormone receptor sensitivity.35 This dimorphism has been demonstrated in the pelvis, where despite similar growth patterns throughout childhood, it is not until puberty when the growth trajectory increases in females, and not until the late twenties when the pelvis attains the most favourable obstetric dimensions. As such, if M2F transgender women undergo hormone therapy at a young enough age, they may develop similar pelvic morphology to natal females.
…
Despite a number of anatomical, hormonal, fertility, and obstetric considerations that require consideration, there is no overwhelming clinical argument against performing UTx as part of GRS. However, the increased radicality associated with the retrieval operation, including a longer vaginal cuff and more extensive ligamentous dissection, potentially necessitates the use of deceased donors. Alternatively, F2M transgender men may offer an alternative donor pool should they accept the increased risk compared with standard hysterectomy. Prior to undertaking UTx in transgender women, further research should be undertaken including cadaveric retrieval and implantations to assess the feasibility of the anatomical considerations discussed herein. Furthermore, it is recommended that animal studies are revisited to identify potential unknown risks and determine whether genetic males can successfully conceive and maintain pregnancy.
The reproductive aspirations of M2F transgender women deserve equal consideration to those assigned female at birth and, subject to feasibility being shown in the suggested areas of research, it may be legally and ethically impermissible not to consider performing UTx in this population.
www.ncbi.nlm.nih.gov/pmc/articles/PMC6492192/