I really think it has more to do with expectations.
When you go to your first appt with your RE you're very raw and scared. You get an impression of that office and how they're going to help you.
If you know up front that babies are allowed/encouraged you expect it and may find comfort in it.
If you find the office to be non-kid friendly (no toys, no pictures of babies you have to walk past) then you expect it to be the one place you don't have to bump into a pregnant belly or baby.
I don't think either is wrong or right but I do think that if you're gonna have a policy and post a sign about it that you need to enforce it to respect your patient's expectations.
If seeing babies bothers you while dealing with IF (and dear lord did it upset me) then you should have the right to find an RE whose practice rules fit what you need to support you thru that struggle. I don't think that's too much to ask.
Re: My thoughts about babies at RE's office.
I agree completely.
We would wait in the hallway, or DH would follow me there on the way to work to sit in the car with DS while I had b/w or u/s. We did what we could, but undfortunately, it did not always work out for us to not have to bring DS.
I agree also about not judging until you have done it.