Criteria set out between landlord and letting agent

Hi, does anyone know if ‘children’ (this includes number of and ages) can be set out as a criteria by landlord to a letting agent? If so, can you refer me to any material? I have been reading Letting agent code for landlords in Scotland and can see that tenants cannot be discriminated bases on on the basis of a person’s age, disability, sex, gender reassignment, marriage or civil partnership, pregnancy or maternity, race, religion or belief or sexual orientation. The way that is it warded I don’t actually understand? Can anyone help?

Ive had many estate agents not sure if coming from the landlords asking the age of the children and telling me a house is to small for me not sure if they can judge that as i desperately looking for anything at the moment. Finding a house is so difficult at the moment.