I fixed this by putting the UNION query in a separate query, named "RSVPositiveTestsParticipants", and then used that in the sub-SELECT of the WHERE IN clause:

SELECT
 demo.ParticipantId,
 contactInfo.infant_name,
 demo.hospital_enroll_site,
 demo.ParticipantId.Cohort,
 contactInfo.medRec_num,
 hsd.admission_date,
 hsd.discharge_date,
 demo.enroll_date,
 st.date as StudyTerminationDate
 FROM study.Demographics demo
 LEFT JOIN study."Contact Sheet" contactInfo ON contactInfo.ParticipantId = demo.ParticipantId
 LEFT JOIN study."Hospital Summary Dates" hsd ON hsd.ParticipantId = demo.ParticipantId
 LEFT JOIN study."Study Termination" st ON st.ParticipantId = demo.ParticipantId
 WHERE demo.ParticipantId.Cohort.Label = 'hospital'
   OR hsd.ParticipantId IN (
       SELECT RSVPositiveTestsParticipants.ParticipantId
       FROM study.RSVPositiveTestsParticipants
   )