I’m just going to say, 90+% of voters can’t tell you the policies of any candidate, included who they vote for. I don’t think this has to shift him right. It just indicates he’s going to cater to them in appearance, but they wouldn’t notice if he adopted her policies or not.

That said, the democratic party does have a tendency to shift right no matter what, so it probably does mean he’ll shift right on some things at least, as if he wasn’t far enough right already.