This double-blind, randomized placebo-controlled trial of infants at risk of allergic disease included pregnant women in New Zealand.
Both mothers and their infants were randomized to take Lactobacillus rhamnosus HN001 (L. rhamnosus), Bifidobacterium animalis subsp lactis strain HN019 or placebo daily.
Mothers took the treatment from 35 weeks gestation until 6 months if breast-feeding. Infants received the same treatment from birth to 2 years.
Infants who received L. rhamnosus had a reduced risk of eczema. No such difference was noted with B. animalis subsp lactis.
Neither bacteria had a significant effect on other atopic diseases.
The authors concluded that oral supplementation with L. rhamnosus reduced the prevalence of eczema, but not atopy.
An example of commercially available OTC probiotic, Align at Costco Wholesale store.
This 2012 study found beneficial effects: Protective effect of Lactobacillus probiotic against eczema in infants persists up to age 4, including for rhinitis.
A differential effect of 2 probiotics in the prevention of eczema and atopy: A double-blind, randomized, placebo-controlled trial. Wickens K, Black PN, Stanley TV, Mitchell E, Fitzharris P, Tannock GW, Purdie G, Crane J; Probiotic Study Group. J Allergy Clin Immunol. 2008 Aug 31.
Image source: Bifidobacterium adolescentis. Wikipedia, GNU Free Documentation License.