She's not an idol, she's a proper TV/movie actress, so normally dating someone shouldn't be a scandal. It's cheating on an existing partner (she hasn't got one), meeting an already married man, being seen with a different man every weekend, etc.
Naturally there would always be (especially in Japan with its whole idol culture) idiots and psychos who only value her as an actress as long as they imagine she's never been in a romantic relationshop, let alone a sexual one. However, she really shouldn't build her career on shallow projects/producers that promote such an image. It would be a dead end career. What would she do once she's too old to be taken seriously as an innocent girl?