Mower, my CFD account is such that I do not get the FC associated with dividends. Hence, if I receive a dividend and the SP drops by exactly the same amount as the dividend payment, then the effect is neutral. Although I cannot confirm it, I suspect that all DMA CFD accounts are like this. Not sure about Market Maker CFD providers as they appear to make their own rules.
Similarly, if I am short on a stock via CFDs, then I have to pay the dividend. However, if the SP drops by the same amount as the dividend payment, then the effect is again neutral.