Providing you are using the correct pairs of contacts on the switches it doesn’t make a difference which way round the white and black wires go. I have tried myself swapping them to prove this as part of an experiment to solve a similar problem to yours.
There are two possibilities I know of:
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If the carriage is bumping into the frame when you are trying to use the home button then it is likely that the software in the motherboard is checking the wrong sets of limit switches when operating the motor. I have written a post on how to work through the Arduino code and amend it so it and the port wiring agree, “Making the XY-Plotter and mDraw work together”, in this forum.
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If the carriage is bumping into the frame only when you are trying to do a drawing but does go home correctly,. then the drawing has been position in the wrong place on the bed, or the stepper switches have been set to other then HHH and will move to a different scale than the drawing. This is because the Motherboard code does not check the limit switches whilst drawing or moving under commands, only when going to the home position. I have written a post on how to correct this “checking the limit switches whilst moving”, in this forum.
There is a third which I haven’t investigated myself but had heard of, and it is if the wires that are screwed into the plugs for the stepper motors are mixed up, the motor direction is altered.