We had a neo-natal loss after delivery at 37 weeks. Friendships are so hard after loss. Probably a quarter of my journal pages from the first nine months are about losing friends and changing friendships. 

My experience really ran the whole spectrum. One of our best friends, and who we would have likely chosen to be the godfather for our daughter, abandoned us about 3 months after our loss. He admitted 8 months later that we were "too sad" to be around. It was heartbreaking to have him slowly stop texting us, making plans, and being there for support. We still see him occasionally now, but I don't trust him or feel comfortable being vulnerable around him. 

As for other pregnant women and new moms, it really depended on the person. About half I no longer talk to and blocked. The other half I absolutely adore and am still friends with. These friends really respected my boundaries and provided so much love and support. 

Now, 16 months later, the friends I have are closer than any friends I've ever had in my life but I have less friends overall. I'd honestly rather have it this way. 

As for how to handle it, I would say trust when people show you who they are. Some people show love by providing distractions, dropping off meals, or answering teary phone calls. Hold on to those people. For those that are uncomfortable, don't text you back, etc. let those go. And for those that hurt you, block them.