WTFBBQ. Tell us what you're doing or stay home.
A bracket on a post is physically attached to it. Maybe you mean not thermally or electrically connected? Why must there be ANY medium between the bracket and post?
What is a decent amount of downward force? What is the temperature range it must operate within and the budget, and lifespan?
Would rubber qualify as a rubber like material? If not what is wrong with rubber? The answer to that gets us halfway there.
Why does it need to be rubber like? Why not duct tape since it solves most problems, or super glue since it's quick and easy?
What about hot glue or bubblegum or pasta or ??
Does the bracket need to be readjusted? With sufficient clamping force even a teflon sheet would allow that.
I'm just giving you some feedback to chew on, why the ideal solution depends on a specific situation that's less vague.