This Wikipedia article includes a definition of classism as:
any attitude or institutional practice which subordinates people due to income, occupation, education and/or their economic condition."
In OPs example sentence
I can't believe that we're allowed to buy our grades now. That seems a bit classist.
Many people feel that there are some things which money should not be able to buy. School grades are an example. If we believe grades should be awarded solely on the basis of academic performance then a policy of allowing students to buy higher grades would be an example of classism, because it allows those who can afford it to buy their way out of studying.
Sometimes a person sentenced to prison may be able to avoid it by paying a fine, provided he is rich enough to do so. Alternatively a person may be able, for a fee, to choose to stay in a more comfortable, better equipped jail. This is not unofficial bribery, but a perfectly above-board practice, which however many people feel is wrong.
The effect of such practices could be described as classist in that they discriminate by allowing the well-off to "bribe" their way out of something.
Another word we could use here is "commercial", in the sense of intended to make a profit.
I can't believe that we're allowed to buy our grades now. That seems a bit commercial.
Allowing people to pay to jump the queue at airport security is a bit commercial.
Usually commercial is not a negative word, but can be used to suggest something which should not be managed for profit, and where everybody should be treated fairly, is actually being run for profit. There is no suggestion the employees are corrupt, but the system itself may be seen as unfair.