Is it permissible to perform Hajj through charitable organizations that require an additional, mandatory amount as a donation to them?

If the association takes the money directly from the pilgrim, there is no harm in that. It is a contract of hire for their transport and accommodation, and the association may then use the money for charities or other purposes. However, if a donor pays the association the cost of pilgrimage for someone who is unable to afford it, and the association stipulates an additional amount, then this is an agency for a fee, which is permissible. The Prophet (peace be upon him) accepted both forms, agency with a fee or without a fee.