Simply put, contemporary films do not win here. Rare is the one that can even get nominated. Rest assured, had La La Land not turned into the Best Picture juggernaut that is has there's little chance Mary Zophres would even be in the running for her colourful wardrobe, however perfectly their vibrant simplicity serves the film. Still, its popularity may make it default choice for many voters.
If any movie can overcome the 'contemporary' stigma in either of the design categories, this is it.
Fun fact: Every since the Critics Choice Awards expanded their honours to include craft categories in 2009, they and the BAFTA and the Academy have matched up every time. It makes it hard to bet against Madeline Fontaine's spot-on sartorial recreations in Jackie, which has already taken those two precursors.
The title of the film itself practically implies all the high-end 60s outfits therein, which may be enough to persuade undecided or uninformed voters.
Florence Foster Jenkins may be a dark horse contender. Consolata Boyle's fussy diva ensembles for Meryl's operatic scenes -- combined with the more numerous but no less showy 40s Manhattanite fashions -- could make it an attractive option. The same argument applies to the old-school Hollywood chic of Joanna Johnston's impeccably tailored glamour garb for Allied. Both films surely have their fans.
Will win: Jackie
Could win: La La Land
Should win: Allied
Should be nominated: Live by Night