Exited game, and from the savepoint when both sims were in the BB household I used the phone to Split From Household and Move, to Streamlet Single, with the gallery-sim. Unlocks category was gone from CAS for them, and I saw no special outfits. Loaded my first sim household on Bargain Bend: they had the Unlocks category in CAS, and I saw a lot of special outfits.
Exited game again, loaded save where they both still lived on lot BB. Moved the whole household to Streamlet Single WC (both of them, my sim and the gallery-sim), and they both had access to the Unlocks in CAS. From there I moved each one in turn into the BFF household WC, by way of the phone, and Manage World/Manage Household - and there they did not; but the one left on Streamlet Single did.
Replicated the scenario with OP's steps:
Made yet a new folder and save, made two sims, placed on Bargain Bend in WC; one entered the Athlete career, got to level 3, which has the first Unlock, the Mascot outfit. Moved them both in with the Goth's, in Ophelia Villa. All in the household had access to the mascot (except the child, for other reasons). Moved only the sport-sim out, by way of Manage Households, into the Feng's, in San Myshuno. No access to mascot outfit for either of them; but to other unlocks. Both default Feng's are high up in their respective careers of business and politics. Loaded save where my sport-sim still lived in Ophelia Villa, moved them alone by way of phone to lot Comfy Cubby, Newcrest. No access to the mascot outfit. Loaded the Goth household in that same savepoint: they all had access to it. Moved my sportsim back to the Goths's; they had yet again access to the mascot in CAS. When going into CAS, the whole household is loaded, both at Goth and at Feng's.
The Athlete career divides at level 4, into Body builder or Professional Athlete.
Workaround:
Move the whole household to which the CAS outfits are unlocked, to whatever lot will be the active one next; and then move out the household members not preferred there, back to original/a different lot. (And not the other way around - to move out the sim the player want the unlocks accessible for).
