New England Pie pumpkins have history before the 1890's
The short answer: Everybody knows, nobody agrees.
Yes, there are plenty of opinions and no real consensus on the subject. Many sources will limit an Heirloom variety to having a beginning before a specific year or time period. This is a bit arbitrary. Heirlooms are more than that. Old and new varieties do not
Cucumbers will cross readily with other cucumber varieties. To save the seeds, I grow designated plants for saving the seeds from, at least 30 plants of each variety for a good gene-pool. Before they come into flower, cover all but one variety with fine Agribon film, and allow insects to pollinate just the one variety. After a large number of fruits have set on them, cover the plant to let the fruits mature and uncover another variety. In the middle of the season I go through, look at the plants and fruits, and remove the least desirable from maturing. This would include fruits that are small, deformed, damaged, and whole plants that are less disease resistant, etc. The seeds are ready to save when the fruits are as soft and ripe as they will become before rotting. This is usually yellow, but sometimes a whitish color. Scoop out the seeds, and ferment for 12-24 hours at 75 degrees F so the gel coating on the seeds is removed. This gel sack prevents or inhibits the germination of the seeds. Then they are dried by moving room temperature air. Done!
The variety pictured here is Double Yield Pickling, a rare Heirloom pickling cucumber that I have been growing for 16 years.