At the crossroads, go straight on. At the crossroads, go straight across. Go straight on at the crossroads. When you get to the crossroads, go straight on.

I find the other answers surprising. ‘Going straight’ without a preposition is very natural and correct in the US At the intersection, go straight. Cross the bridge, then go straight for 5 minutes. We might use a verb other than ‘go’, however, and we’re less likely to use ‘crossing’ by itself. It sounds vague to me. For example: Continue straight at the railroad crossing.

No, you wouldn’t use at in this context. The dog was running straight at me. The ball came straight at me.