A client asked me to make this cake for her and I can't figure out how to get the ribbons straight (enough). I have the Wilton ribbon cutter so I know the actual ribbons I'm making are straight.

You'll note that the ribbons are a bit off in the picture and I'm ok with them being off just not as wavy as mine were.

If you need to, cut your ribbons up and work with smaller sections.  They'd be easier to handle and you won't risk them getting wonky as you're applying.

I think those are real ribbons, they seem too shiny to be fondant.

But if you want it all edible (I would), you can either try a wax paper transfer or like the pp suggested, use the intersecting points to create "sections" and lay it in pieces.

I think they are gumpaste - if you look closely, there are 2 little 'nicks' which look like they could be joins.  If I was you, I would use a long paintbrush and paint water onto the cake in a long smooth line then apply the gumpaste to the cake.  If you 'lower' it on from the top, then hopefully it should stick to the line and help maintain the straightness.

They are gumpaste/fondant.  Real ribbon would not lay nicely with those curves and bends.  And you can see the joins like snowflakebunny23 said