I won't get into the weeds with this topic, but it has been a matter of debate for many, many years. While it has been a very long time since I visited this subject, the public health codes in most states have prohibited the use of wood as food contact surfaces in foodservice establishments. This prohibition was based largely on the belief that wood surfaces are more difficult to clean/sanitize than the surfaces mades from other materials. Given the porosity of wood vs. other materials, this seemed to make sense...however, closer evaluation of surfaces made from materials that are approved for food contact revealed that they had many surfaces irregularities that could also easily harbor microorganisms and unless properly cleaned and sanitized lead to the formation of biofilms.
Over the years I recall reading a number of papers on antimicrobial factors associated with various woods; some papers corroborated previous work, others reached different conclusions. This isn't surprising, there are so many subtleties associated with experimental protocols that can impact outcomes and make direct comparisons challenging, if not impossible. As an examples some work was performed by introducing bacterial cultures directly on the surfaces of various species of wood, while others made extracts from sawdust or introduced sawdust into culture tubes. (I said I didn't want to get into the weeds, but it appears that I am knee deep...sorry!).
To wrap this up, clearly some woods do have antimicrobial properties, but I am not sure that we should be using cutting boards made from wood solely because of this. Whatever materials we use good hygienic practices are a must! These practices are to clean AND sanitize food contact surfaces...please note, this is a two step process: clean and sanitize...you cannot adequately sanitize a dirty surface. (As a quick aside, years ago a food processor called me and ask if I would help him. He company made coleslaw and other prepared salads. His problem was that his product wasn't getting anywhere close to the shelf-life that was expected. Early one morning, prior to start-up, I did a walk around his facility...the place reeked of chlorine (it was obvious they were using sanitizer!). I swabbed the surfaces of various pieces of equipment. Two day latter I went back and told him the chopper was his problem...it turned out that the chopper was difficult to break down and clean, so the new cleaning crew was giving it a heavy shot of sanitizer solution but they did not routinely break it down and clean it before sanitizing. Once this problem was resolved, the shelf-life of the product dramatically improved.)