Re-write as an EXISTS, rather than IN sub-query:

UPDATE #branch_users

SET greenlight = 1

FROM #branch_users As B

WHERE EXISTS (

  SELECT *

  FROM appian.dbo.users USERS

    JOIN dealerinfo.dbo.v_DealerBranches DB ON DB.dlrcode = USERS.dlrcode

    JOIN dealernet.dbo.v_loginlog LL ON LL.auid = appian.dbo.udf_A

  WHERE DB.branchid = B.branchid

)