～が前を歩いていました
I read this answer but I feel like this case is different because 前 is not a place but a relative position. I'm used to seeing に used for position, for example when giving directions "左にあります". What would be the difference if I were to say "～が前に歩いていました"? Are we using を because 前に could be confused with "before" in time? When should we use を for the position instead of に?
The answer in your link applies to your sentence, too. See this question, too. 前 is a relative place that may move along with the "parent object", but it's still a place. If someone keeps walking in front of you for some time, を as a location marker should be used, because he is keeping inside your 前. The same is true with 後ろ, 右, 下 and so on.
On the other hand, に used with a verb of motion marks a destination. For example, ビルの前に歩く means walking to the front of a building from some remote place (EDIT: ビルの前まで歩く is more common for this meaning). ビルの前を歩く means walking in front of a (large) building.
The particle を is used with certain verbs of motion, such as 行く, 歩く, and 走る, to indicate where someone or something moves through. It is said to indicate a point of passage. It doesn’t matter whether that point is expressed in absolute terms or relative to something else.
The particle に, on the other hand, is used with verbs that describe the presence or existence of someone or something, most typically いる and ある.
〜の前に歩いていました is not totally wrong because of the compound form 歩いている, but its focus is on いる (presence) rather than 歩く (motion).
I can think of an example like this.
玄関を出ると、家の前にカブトムシが歩いていました。
Although this sounds a bit awkward and is probably considered ungrammatical, it’s understood with little difficulty in everyday conversation. The main focus of the main clause is that there was a beetle in front of the house. It happened to be walking but was, for the obvious reason, too slow to look “passing” in front of the house when you found it. It’s hard to imagine a similar situation with people walking.
You can still use を to describe the same scene.
玄関を出ると、家の前をカブトムシが歩いていました。
Actually, this sounds more natural however slow the beetle may have been. The sentence puts greater focus on the passing of the beetle, and that’s usually what you would expect when you choose to say 歩いていました instead of just いました.
By the way, で may also be used with 歩く.
玄関を出ると、家の前でカブトムシが歩いていました。
In general, this particle is used to indicate a place where some action occurs, and therefore, the above sentence puts greater focus on the beetle’s action of walking and where that was happening, compared to the earlier sentence with を.
When 歩く is not in the form of 歩いている but in its basic form (i.e. 歩く), it is not usually used with に.
The most natural choice would be を.
毎日、家の前を歩きます。
You could use で but it changes the nuance.
毎日、家の前で歩きます。
In this sentence, walking is seen as an action in its own right, or something you do for the sake of it, perhaps as part of your physical exercise, rather than as a means of moving from one place to another, and that action takes place within the boundary described as 家の前.
に is not usually used with 歩く even in cases where it would indicate a destination. 駅に歩く sounds weird. 駅まで歩く sounds much more natural.
