Taken from cancer.org, I’m just listing the vegan friendly foods from that page!
Bread, cereals, and grains
White breads, waffles, French toast, plain white rolls, or white bread toast
Plain pasta or noodles
Crackers, zweiback, melba, and matzoh (no cracked wheat or whole grains)
Cereals without whole grains, added fiber, seeds, raisins, or other dried fruit
Use white flour for baking and making sauces. Grains, such as white rice, Cream of Wheat, or grits, should be well-cooked.
Include the above grains in casseroles, dumplings, soufflés, cheese strata, kugels, and pudding.
Avoid any food that contains
Brown or wild rice
Whole grains, cracked grains, or whole wheat products
Corn bread or corn meal
Vegetables and potatoes
Tender, well-cooked fresh or canned vegetables without seeds, stems, or skins
Cooked sweet or white potatoes without skins
Strained vegetable juices without pulp or spices
You can also eat these with cream sauces, or in soups, soufflés, kugels, and casseroles.
All raw or steamed vegetables
All types of beans
Potatoes with skin
Cabbage, broccoli, cauliflower, Brussels sprouts, and greens
Fruits and desserts
Soft canned or cooked fruit without seeds or skins (small amounts)
Small amounts of well-ripened banana
Strained or clear juices
Small amounts of soft cantaloupe or honeydew melon
Cookies and other desserts without whole grains, dried fruit, berries, nuts, or coconut
Sherbet and popsicles
Serving suggestions include gelatins, milk shakes, frozen desserts, puddings, tapioca, cakes, and sauces.
All raw or dried fruits
Prune juice, prunes, and raisins
Mild salad dressings and oils in small amounts
Ketchup and mild mustard
Spices, cooked herbs, and salt
Sugar, and syrup
Pickles, olives, relish, and horseradish
Keep in mind that low-fiber foods cause fewer bowel movements and smaller stools. You may need to drink extra fluids to help prevent constipation while you are on a low-fiber diet. Drink plenty of water unless your doctor tells you otherwise, and use juices as noted above.