Aromatic cedar is strong enough for the framing you want to do. By A.
cedar not being strong enough for furniture framing, it is meant that
for a chair, a table or anything that will require a shifting weight,
then A. cedar may be compromised as for as the strength. It splits
easily, so any stress or sheer force has a tendency to cause it to
split or crack. Your closet cabinets don't fit that category of use.
Also, since it is so resinous, glued joints, and doweled joints, of
stressed furniture have more of a tendency to fail. Pegged mortise &
tenon joints work well, and usually the exposed pegs are especially
appealing since many A. cedar projects often times suit the rustic
If nailing your framing, air-nailing cedar framing is favored, also
.... less likely to split as when using a hammer.