Are both examples’ ‘cuts across’ equivalent to ‘is contrary to’ or ‘is against’?
Both involve the same metaphor of cutting across existing natural lines of cleavage, as when we speak of cutting across the grain of wood or meat:
When we speak of issues or votes cutting across party lines we understand 'party lines' to be the 'lines' which divide the parties. On most issues people's attitudes follow party lines:
But some issues divide differently: they cut across party lines: Note that the 'party lines' we speak of here are not the same thing as 'the party line': the official position a party takes on a particular issue and its rhetorical 'line' of argument for supporting it. When an issue cuts across party lines it is not (necessarily) contrary to the parties' positions on the issue; it is 'contrary to' the usual lines of division between parties.