Last time I did that they insisted they wouldn't. They insisted I could make the payment at a private bank nearby; I refused to route my tax payment through a private company whom I had not consented to dealing with. "You're demanding payment, here's my payment, now take it or I risk losing my house for non-payment." Took a lot of ranting on my part for them to consent to accepting tax payment in cash, and they threatened to charge me for counting it.
You did point out that the money says legal tender for all debts public and private?
Good for you!
Actually, I paid my property taxes Monday with cash! First time I did it. I called first and they accept cash. Apparently, they will only accept cash from some people, so I decided to try it. It did feel a little strange though.