I search google and I only see references to the facebook post saying he had F rating from NARAL. If he did, maybe he has evolved on this issue, or maybe he didn’t realize what the plates funds were used for at the time of sign. Maybe he thought he was allowing freedom of expression. We can confirm he is not anti-prochoice through his voting record

“Tim Kaine has a perfect 100 score from the NARAL folks, and a perfect 100 with the gay-left Human Rights Campaign. ”

This is also quite promising “after two years in the Senate, Tim Kaine has a perfect zero on the conservative scale.”