vocabulary - meaning: cut across something

(1) Support for environmental issues cuts across traditional party lines. (Cambridge dictionary)
(2) opinion on European integration still cuts clean across party lines (Collins dictionary)

Are both examples’ ‘cuts across’ equivalent to ‘is contrary to’ or ‘is against’?

Answer

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:

_{The flank steak image is from theenchantedcook.blogspot.com, the saw image is from cmtutensili.com.}

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.