How to Implement IEqualityComparer<PointF> With Tolerance

Instead of defining the tolerance by the distance, you could place the points in a grid.
If two points are in the same cell, they're considered equal and have the same hash code.

public bool Equals(PointF pt1, PointF pt2)
{
   return GetCell(pt1.X) == GetCell(pt2.X)
       && GetCell(pt1.Y) == GetCell(pt2.Y);
}

public int GetHashCode(PointF pt)
{
   return GetCell(pt.X) ^ GetCell(pt.Y);
}

private static int GetCell(float f)
{
    return (int)(f / 10); // cell size is 10 pixels
}

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Thesis: There is no implementation of Equals and GetHashCode that meets your requirements.

Proof: Consider the following three points, A, B, and C:

As per your requirements,

Equals(A, B) == true              // (i)
Equals(B, C) == true              // (ii)
Equals(A, C) == false             // (iii)
GetHashCode(A) == GetHashCode(B)  // (iv)
GetHashCode(B) == GetHashCode(C)  // (v)
GetHashCode(A) != GetHashCode(C)  // (vi)

But from (iv) and (v) follows

GetHashCode(A) == GetHashCode(C)

and thereby

Equals(A, C) == true

which contradicts (iii) and (vi).

Since Equals and GetHashCode cannot return different values for the same arguments, there is no implementation that meets your requirements. q.e.d.