I've been canning tomato puree for 30 years. I've tried a few different routines. The one that I like the best is as follows:

Wash the tomatoes (varieties such as Speckled Roman, Heinz, Grandma's Paste).

Cut out any imperfections and quarter.

Boil and when the tomatoes are soft use hand blender to create puree.

Continue to boil until reduced by almost half till it is the consistency of typical tomato puree sold in stores.

Add 1/2 teaspoon of citric acid per quart.

Can in boiling water bath for 45+ minutes.

Using this method I do not remove the skins or seeds. The skins are not detectable after blending with the hand blender. You can detect a few seeds, but not many.

However, I notice the NCHFP says to remove the skins and seeds. I've heard in the past that the skins and seeds only add to the acidic level, so I'm assuming what I am doing is acceptable. Maybe Dave and others can weigh in on this thinking. TIA : )