I have quilts more than 10 yrs old with invisible thread that have held up fine thru washing and drying. I used a cone of inv.thread from joanns
As far as the use in baby quilts, the concern is that thread ends could wrap arourd a finger or toe and cut off circulation. if you're careful trimming it shouldn't be a problem. monofilament is/was used in a lot of childrens clothes. The only problem i've ever had was with a purchased sleeper, a thread did wrap around my DD's toe but no serious damage was done before we found it. Could happen with any thread really.