How does bringing babies to classes make the person, i.e. the student who brought the baby to school, feel?
I think in general, people realize that there are situations beyond one's control where things that are less than ideal are accepted in order to allow education to continue.
If you google-search for "Prof holds baby" you'll get a lot of hits for cases in which the lecturer holds the baby to let the student pay attention to the course material.
How does this make one "feel"?? I suspect that the person would feel much like they would in any other situation where one is different from the majority of the people in the room. The person might do fine, so long as the baby behaves well, and if the baby starts crying, like babies do, you may feel differently. Same as if you brought a baby into a fancy restaurant on a Saturday night -- you might choose to be ready to leave if things go wrong and those in the room can't tolerate it. If you're sensitive, you might not like being the center of negative attention, or you may be a person that's fine with it.
I suspect that if it's necessary to continue one's education, it might be well tolerated. Further, the person who does it might feel proud that they're able to work hard and pull off a tough situation successfully. It might not be well tolerated if it's every class and the baby is fussy, and the person with the baby might feel like they wanted to disappear.