How far away would they have to be for you to not have a special procedure requiring a turn.
I presume you are considering the case of flying straight ahead and then clearing the obstacles ? or else running a turning escape
Your question can't be answered simply as it doesn't define the Type and situation geometry.
What we would do is run an analysis for the case and see if we clear the obstruction at the weight for the conditions. If so, OK, if not, then the choice is either to reduce the weight until it is OK .. or turn to make the problem go away.
The minimum distance from the runway head to the obstacle will depend on the V2 which determines turn radius. Run the takeoff to a minimum 50ft NFP clearance and then one can commence the turn. The relevant obstacle consideration splays will then determine how far away the obstacles have to be .. ie the position in the turn where the splay edge sits at a NFP clearance of 50ft is the critical consideration. Simple geometry then gives you your required answer. For an early start turn, the distance to the obstacle is not overly great ..
The process may sound a tad complicated but it really is very straightforward ...