Explanation

“To go out on a limb” alludes to climbing out along a tree limb — an exposed, precarious position. Figuratively it means taking a bold stand that others do not share, i.e. adopting a daring position that goes against the popular view — option (c). Options (a) and (b) wrongly substitute “convenient” for “daring”, and (d) reverses the idiom’s contrarian sense.