Step 1) Get out of Gigai.
Step 2) Change clothes of your spirit form.
Step 3) Step back into Gigai.
Step 4) Change clothes in Gigai.

I think the big problem (and what Matsumoto was referring to) is finding someone who makes modern casual clothes for spirits. Urahara might be the only candidate. I suppose a spirit could wear material clothes, but that would look really funky to mortals and they'd have to abandon them anyway to enter Gigai, meaning they'd be naked next time they got out...