Is there any standard for evaluating the acceptable levels of boric
acid in rubber wood used in kitchen utensils and cutting boards (or
wooden children's toys)? If so, what is the maximum level allowed in
the wood? A clearly defined standard from the US, EU or some other
developed country/region would probably be sufficient.

Is rubber wood lumber from rubber trees?  Neil

Yes, it is wood from rubber trees. It is commonly used for
wood-products manufactured in Malaysia, Vietnam and Thailand.

Borate preservatives are readily soluble in water, are highly
leachable, and should only be used above ground where the
wood is protected from wetting. When used above ground
and protected from wetting, this preservative is very effective
against decay, termites, beetles, and carpenter ants. Borates
are odorless and can be sprayed, brushed, or injected. They
will diffuse into wood that is wet; therefore, these preservatives
are often used as a remedial treatment. Borates are
widely used for log homes, natural wood finishes, and hardwood
pallets.
The solid or treating solution for borate preservatives
(borates) should be greater than 98% pure, on an anhydrous
basis (AWPA P5). Acceptable borate compounds are sodium
octaborate, sodium tetraborate, sodium pentaborate, and
boric acid. These compounds are derived from the mineral
sodium borate, which is the same material used in laundry
additives. (Wood HAndbook,1999)

Otherwise my professor said that it is one of more environment
friendly wood preservatives. It is one of more environment and human
friendly preservatives!