How do I advise parents to be about outdoor BBQ smoke and indoor wood fired chimney smoke?

Red Nose does not have specific guidelines about combustion heaters or BBQ’s, however as with any fuel based heating in the house it is important to ensure the air quality within the home is good. 
The smoke from combustion heaters is different from tobacco smoke on its impact on baby, specifically due to the effect of Nicotine on baby. However, both are dose related - the greater the exposure the greater the risk. 
As with gas heaters, airflow is important, & most Government Environment Departments recommend having a window open slightly to allow for this. 
 
While I am not aware of any relationship between smoke from wood fire combustion heaters & sudden infant death, however, can smoke cause long term irritation to airways, particularly with babies & children.
Large exposure (eg house/bush fires) can cause carbon monoxide poisoning. 

Local State Health Authorities have information about safe use of heaters.
What can you do to minimise air pollution from your wood-burning heater?
Check your wood-burning heater conforms with the Australian Standard (AS/NZS 4013) and that the heater and chimney are installed in line with any council-specific building requirements. 
Ensure fresh air enters the room to prevent carbon monoxide build up.
from NSW Health - Environment. Fact Sheet.   
 https://www.health.nsw.gov.au/environment/factsheets/Pages/wood-smoke.aspx -  
see link for full information.

Most BBQ’s also create smoke & should not be used indoors or in confines spaces.
Limit smoke exposure, especially for babies & young children.

I hope this provides information for you to discuss with your client.
The information provided in the link from NSW Health also has a link to resources which may be appropriate for you to refer your client to.