>It is absolutely your responsibility to make sure that it is safe to do so.
In aviation safety, it has long been established that, regardless of how clearly you establish who is responsible for what, if reality is such that people frequently can't actually carry out their responsibilities effectively, then you'll end up with disasters; disasters where you'll have someone to officially blame, but disasters nonetheless.
This is quite relevant to many pedestrian-car interactions. The problem with right turns over crossings where pedestrians have priority, is that in many situations, even if the driver is responsible for ensuring the turn is safe, it isn't possible for them to do so effectively. In many California right-on-red situations, for example, the driver is responsible both for ensuring that the road to their left is clear, and that the crossing to their right (and in front of them) is clear. Traffic, visibility, and speeds often mean that ensuring the road to the left is clear requires the driver to be looking far to their left until almost immediately before turning, and then accelerate quickly. At the same time, ensuring crossings are clear requires them to look both ahead and to their right, and similarly, visibility and layout often mean that the relevant portion of the crossing can go from being clear to blocked almost instantly, so the driver must be looking to their right immediately before turning. The two responsibilities conflict, and in order to turn, the driver must choose which risk to prioritize: if they prioritize checking for pedestrians, they'll increase the risk of a two-vehicle collision, and if they prioritize checking for vehicles, they'll increase the risk of hitting a pedestrian. Not turning is an option, but at least in California there would be considerable pressure culturally and from other drivers to do so, potentially to the level of threats and violence. It is not a good situation to put someone in.
The only time I have ever been hit by a car as a pedestrian was when I was very mildly hit by a driver turning right immediately after I stepped into a crossing. Legally, she was entirely at fault, but as I already felt the crossing was problematic, she was very apologetic, and I was entirely uninjured, we just didn't report it. And in hindsight, the intersection was just horrible. She couldn't see me because I was to her right and would have been obscured by trees and parked cars until immediately before entering the crossing; in order to avoid being hit by traffic, she needed to look to the left. While not legally my responsibility, in order to see her, I would have needed to look behind me before entering the intersection, but I also needed to watch carefully for cross traffic. In utterly bad design, despite heavy traffic and a 35mph speed limit, pedestrians always had legal right of way at the crossing, so she couldn't even have waited to have right of way.