But you are inferring that big teams would turn up their noses at whoever sponsored them according to the nature of their business, toys or otherwise and I think that's highly unrealistic.
If the money's there no team would turn it down, and they wouldn't give a toss whatever product it would be they're advertising, providing there's no conflict of interest.
Even Enzo Ferrari, who'd previously made a point of refusing any offer of sponsorship from non-automotive related suppliers eventually gave in when the Marlboro money came along.