Is it possible for a parent to apply for naturalization in the U.S.
(using form N-400), without making their children under 18 years old
No. The process for US permanent residents, under 18, living in the US in the legal and physical custody of a US citizen (biological or adoptive) parent, to become US citizens under INA 320 is automatic and involuntary as soon as all the conditions are simultaneously met. Neither the parents nor the child can choose for the child to not become a citizen if the conditions are met. The only way to prevent it from happening is to prevent all the conditions from being met simultaneously, e.g. delay the parent's naturalization (i.e. taking of the oath) until after the child turns 18, have the child relinquish US permanent resident status, have the child not reside in the US, or have the parent give up custody of the child, etc.
For example, the parent might not want the children to become U.S.
citizens as that would cause them to be liable for tax in the U.S. for
the rest of their lives, even though they will be living somewhere
In order for a child to automatically become a US citizen under INA 320, they must already be a US permanent resident, and if they are a US permanent resident, they are already subject to US tax on their worldwide income no matter where they live, unless and until they file I-407 to relinquish their permanent residency. So in this sense, whether the child becomes a US citizen or not doesn't make a difference, except that renouncing US citizenship is more expensive than relinquishing permanent residency.