I understand the basic concept that a larger sensor doesn't change DOF.

Just because you understand a certain proposition does not make it a correct proposition. In this case, your understanding is incorrect, given some unspoken assumptions that almost all DoF calculators make:

Images taken with the

• same focal length with the
• same lens at the
• same aperture from the
• same shooting position will be
• enlarged to the same display size

every DOF calculator I can find changes the results when I change the sensor size. Why?

Because every one of them assumes you will display all images at the same display size, usually 8x10 inches or 8x12 inches from a distance of 10 inches.

To get to the same display size an image from a smaller sensor must be enlarged by a greater factor than an image from a larger sensor.

The more you enlarge, the larger you make the same blur measured as it was projected by the lens onto the sensor.

Furthermore, I've tried two calculators that support teleconverters and reducers. One of them shows no difference in DOF and the other one does. Which is correct?

The Purple one.

Seriously, until we know what all of the other assumptions are for both of them, we have no way to properly answer the question.

Update in response to a comment from the OP:

Assume that I insert a teleconverter between the lens and camera. I change nothing else. Does DOF change?

Yes, for three reasons.

• Focal length actually changed with the addition of additional refractive surfaces between the front of the lens and the sensor.
• Because focal length changed but the entrance pupil size did not change, the f-number is also changed. For a 1.4X TC the f-number is one stop higher with the same size e.p. For a 2X TC the f-number is two stops higher. For a 0.71X reducer, the f-number is one stop lower (0.71 is the reciprocal of the square root of 2).
• Unless you refocus your lens after changing the focal length, your focus distance has also changed and your subject is no longer in focus.