There is not a single study proving unvaccinated children are a risk to the immune-compromised. What we do know is that anyone with cancer should NOT be around a recently vaccinated person because they shed live viruses for weeks.
Measles virus sheds for 1-13 days after vaccination:
Measles outbreak among the vaccinated:
Varicella transfer after vaccine to pregnant mom:
Rotavirus vax shedding:
There’s more where this came from, but you get the idea!