I agree that both words are good, but there is a difference.

Whitelist means that anything explicitly listed (in the "whitelist" or "allow list") is allowed (or included, etc) and other stuff is disallowed (or excluded) by default (although in some cases, a program (or something else) might ask instead of forcibly blocking access). It is a compound word; you should not use a space or hyphen. (Using two words "white list" may be appropriate when you are refering to colours, e.g. the white list includes the list of whatever documents are to be copied on white paper, or "white list" might mean the list that is printed on white paper.)

Allow list (I do not like the compound word; I think they should be separated and it looks better that way) is the list of what is allowed. (So, normally, this would mean that other stuff is not allowed, so it is still whitelisting.)

In situations where colours would be involved and using words such as "whitelist" would be confusing, such words should be avoided, in order to avoid confusion.