はそっちのけで / をそっちのけで

はそっちのけで and をそっちのけで mean "pushing X aside": someone leaves the thing they ought to be doing and throws themselves into something else. The neglected thing is a noun, and what they do instead follows. The speaker nearly always disapproves.

The neglected thing is usually a duty: work, study, housework, the people you are meant to look after. そっちのけ is そっち "over there" plus のけ from しりぞける退ける "to push aside".

は and を are both common and mean the same here. は sets the duty against what is being done instead; を simply marks it. In speech the particle can drop: べんきょう勉強そっちのけであそんでいる遊んでいる.

The pattern works in speech and in writing. A more casual way to say the same is ほったらかして: しゅくだい宿題をほったらかしてあそんでいる遊んでいる.