I am currently 12 weeks pregnant after a FET while still nursing my two year old. My clinic also would not proceed unless I stopped but I lied in order to move forward with our transfer. I did not feel comfortable weaning my son for a pregnancy that was not guaranteed. I didn't come to the decision lightly or easily and after a lot of research I felt comfortable lying so that we could proceed. I felt the meds I took were safe to take while breastfeeding, but to be honest I don't know anything about the meds for a fresh cycle and breastfeeding because that didn't apply to us so I didn't look into it at any length. My guess, though, is that even if my FET had failed I would have continued to nurse my son through a fresh cycle. I think there is one med (forgot which one) that isn't as safe as the others but it has a short half life so you would just need to wait so many hours after the med before breastfeeding again. Like I said it didn't apply to us so I didn't look into it that deeply and don't know the specifics. I sort of rationalized that even though taking hormones while breastfeeding wasn't ideal, it's only a short period of time so I didn't feel the risk was there. I mean if I was giving my son cows milk that wasn't organic, think of the hormones those cows are treated with that he would be exposed to!!!!! That seemed worse to me in the long run than just a few weeks of me taking estrogen and progesterone. That was sort of my thought process anyway. You won't find a ton of resources online, but if you spend time digging, you will find enough to be able to make an informed decision.
My doctor's reasoning for their strict no breastfeeding policy (she flat out said it had nothing to do with the meds) is because some women have elevated prolactin levels throughout lactation which could interfere with your body's ability to implant an embryo, but most women don't have that issue once you are nursing a toddler. Nursing an infant is very different than nursing a toddler as far as it's effects on moms hormone levels. She said if she lets everyone breastfeed through cycles their success rates would go down because there are many women who will have trouble conceiving while their hormones are not regular yet. Oh ok, so I have to wean my son before he is ready because of your success ratings?!?!? I don't think so. I do know some friends who didn't conceive until they fully weaned, so I do understand there is some truth to what my doctor had said. But it's not a blanket statement, many women can and do get pregnant without issues while breastfeeding. I've had regular cycles for quite a long time so I didn't feel that I would have the same trouble. If I didn't conceive I know it would have been because it was not a quality embryo and not because I was nursing my son. Kellymom had good resources to figure out who might need to wean in order to conceive and who wouldn't.
Good luck in whatever you decide. I'm here if you have any questions.