In large part, it depends on the sequence of the transaction and what kind of transaction it is. That will determine whether the transaction will be completed and how it will be paid for.
Let's look first at Sebastian's post. He has had the experience of pumping gas, offering legal tender, and being allowed to drive away with free gas because the cashier refused to take the tendered cash.
In this case, just as in the case of consuming a meal, the obligation to pay is created by consumption of the goods prior to paying for them. In this situation the merchant can either accept the tendered cash, or he can refuse the tendered cash for policy reasons of his own. But insofar as the law is concerned, you have tendered lawful payment, which means you have offered to pay the debt you have incurred with legal money. If the merchant refuses to accept this payment, then you are relieved of the debt. Your duty and obligation is to tender lawful payment, and if the merchant refuses it, your debt is discharged. US money is legal tender.
On the other hand, let's say you go to the grocery store, pick out some items, and go to the checkstand, where the cashier rings up the total. You present a $100 bill, but the cashier refuses to accept it. In this case you have not "consumed" the goods, and the transaction can simply be cancelled. The store takes back its goods and you leave without them.
The same concept would apply to the condo situation, you might think, but not really. This is because buying real estate involves a written contract, and the terms of that contract are enforceable once it's been signed.
Therefore, so long as there is no provision in the contract that specifies that payment shall be made ONLY by cashier's check or "certified funds", then tendering cash fulfills the requirements of the contract, because it is "legal tender."
As I said, you must read the contract carefully and REMOVE any provisions that prevent tendering cash, *if the other party will agree to that amendment*, in order to preserve your ability to pay cash. This is because a contract is a "meeting of the minds" and a binding legal agreement, so one side cannot unilaterally change a provision of the contract without the approval of the other party.
However, if you strike out a provision in a contract, initial it, and give it to the other party and give them adequate time to read and consider the change, and they DO NOT OBJECT to the strikeout, then their right to object can be lost under the concept of "estopple." By giving them notice of the changed provision, by, for example, striking out the "only by check" or by adding "cash" to the provision about forms of payment in the presence of a representative of the other party, you give them due notice and opportunity to say "hey, wait a second, I have to check this change with my boss" or otherwise object to the change. If they fail to perform their due diligence, then they may have waived their right to object.
It's all something of a game, but if you play by the rules, and there is NOT explicit language that PROHIBITS tendering cash, then tendering cash is ALWAYS a legal option, and in the case of a contract, tendering cash fulfills your side of the contract, which obligates them to fulfill their side, or be in breach of contract.
The point is that unless YOU have agreed to tender payment in some form OTHER THAN cash, in advance, you cannot be compelled to pay other than cash. But then again, the merchant (or the rail company) is also not obligated to provide you with service or goods unless you pay in their preferred form of payment.
However, if they accept cash as legal tender, but they seek to restrict the denomination of the bills they will accept, it is THEY who take the risk of having to take the loss if you have consumed the goods or services and you tender payment using lawful currency of any denomination.