As I understand the the rules you can enter a space with a crate on it.

Can you claim a crate in the campaign game if an enemy figure is occupying the space where the crate is placed, but has not claimed that crate yet.

Yes. You have to block the crate and all adjacent spaces to make the crate inacessable. So just an enemy standing on the crate is not enough to block access to it.

From Rules Reference Guide:

During a campaign, heroes can interact with a crate to claim

the token and draw a Supply card.

And

Interact

Figures can interact to perform a variety of different tasks. For

example, a figure can open a door by performing an interact.

• A figure can perform an interact as an action.

• A figure must be in the same space as or adjacent to a token in

order to interact with it.

• During a campaign, a hero can interact with a crate token to

claim the token and draw one Supply card.

• Mission rules will often list different tasks that can be

performed by interacting, such as using terminals or retrieving

tokens.

• If the mission rules have an attribute icon in parentheses

after the target of the interact, the figure must pass the

corresponding attribute test in order to resolve the effect of the

interact.

Related Topics: Actions, Activation, Doors, Crate Tokens,

Retrieving Tokens, Supply Cards, Terminal Tokens

It is sufficient to be adjacent to the Token to make the interact action. The hostile figure on the token does not affect this at all.