Are parents allowed to be with baby when it is undergoing circumcision?

Depends upon surgeon. Some dr.S feel comfortable for parents to be present, others don't. Also depends upon hospital or medical office policy. I personally always ask if parents wish to be present. However we make sure that parents are up to it, and tell them to either be prepared to sit down if or remain seted if they feel "queezy".
Usually Yes. There should be no problem if you ask. But some do not wish to see the procedure.
Depends. These are often done in a procedure room in the mornings when docs are doing discharge rounds. In that setting, hospital rules would allow parental participation unless there was another baby having a procedure done at the same time. Patient confidentiality rules then kept them out. A few were curious, from my vantage point, I enjoyed their participation, most parents did not ask.
Here are some ... Usually, parental presence at neonatal circumcision is not allowed for better aseptic environment, avoiding incidental parental fainting from vasovagal reflex by exposing to blood, etc. But, to serve political correctness, parents are allowed by sitting in a "far" distance.