I climbed during my first pregnancy. I found hormones were the biggest blocker to routes, so I stopped those very early (8 weeks), as I had an overwhelming feeling of insecurity. I've just found out I'm pregnant again, and have dropped down expectations again.
I kept up bouldering. I didn't feel safe doing anything where I might fall (by which I mean those silly falls that you don't expect), so I often didn't do the last move, and instead did easy routes (nb all indoors), and just enjoyed the movement. You also have to think about your exit - e.g. having an easy way to climb down.
As bump got in the way, I stuck to low level traversing on circuit wall, for a long time. I had a very enlightened physio who said it was a great way to stretch your back (all that twisting). As you go on, you have to be careful to not make too much use of your increased flexibility.
My abs hurt a lot in pregnancy, but I was very fit when I got pregnant and had been climbing a lot, so I suspect they were just very tight.
I went back to climbing about 12 weeks post partum, in the day time, with baby on playmat at the wall. It was a lovely way to spend mat leave, until she learnt to move. You could easily pop down and play/ feed baby, whilst still feeling like you've got a bit of "you" back. She's 2 now, loves the wall, and is climbing to teddy herself!