There are two parts to your problem. One is about unsupervised older children in the baby area - that should probably be addressed with the organisers. I don’t think anyone should have preschoolers where they can’t be seen at all times.
The second is about mild illnesses, here YABU. If you really don’t want your child to pick up coughs and colds then you need to stay away from baby groups. That’s obviously unrealistic from a maternal mental health POV, but you need to make a judgement call.
There is a school of thought that exposure to common viruses is beneficial for young children who are building an immune system. Yes the viruses change over time, but usually slowly so having had a different strain of a virus usually helps the body’s immune response. Part of the issue with covid is that it is significantly altered from previous coronaviruses in the population (possibly because it has mutated in an animal host, likely because it has been tampered with in a lab- I’m going with the accidental release theory based on my PhD in the life sciences). We don’t have any previously encountered illnesses like this one so it’s much harder for the body to fight, it spreads quickly, immune systems go into overdrive trying to kill it (which is largely what puts people in hospital, same as the 1919 flu).
Some academics believe that some more serious illnesses have some connection to how well tested our immune systems have been. Note, that doesn’t mean there is a causal link, but that in general, being exposed to mild infections may overall be protective. Covid has made us lose all perspective of childhood illness, and indeed my own (older) children appear to have lost some natural immunity through not having general population exposure to common illness.
TL;DR - common childhood illness is good for children.