From a Citi's brokerage services contract: "accept and agree to be bound by its terms, as amended and supplemented from time to time by Citibank" Is it normal to impose requirements like this? As much as I understand, they can change the contract in whatever way they want and don't even ask my permission to do so?
Yes. It is normal. Almost all credit card agreements are drafted in that way.
Implicitly, however, changes in the credit card agreement must be prospective only and cannot alter rights that vested under prior versions of the agreement (e.g. charging a lower interest rate).
A key factor is that a credit card agreement is terminable at will with respect to new transactions by either party by ceasing to make new transactions under the new terms, or ceasing to authorize further transactions under the old terms.
As much as I understand, they can change the contract in whatever way they want and don't even ask my permission to do so?
They don't need your permission simply because they are happy for you to go if you don't agree. It's an ongoing "take it or leave it" contract.
What you agree to is to check every terms update coming down from them, make up your mind if you still agree and quit if you don't.