Jay, Holly, and Lion were respected, but that was before everyone knew, the same goes for Mistyfoot and Stonefur.
What happened with Mapleshade and her kits when they were found out? Their mother was attacked in front of them and called creatures by the cat who loved them days ago before she knew.
This won't happen to Dovewing and her kits considering that Tigerheart/star II actually cares about her more than Appledusk with Mapleshade, but because everyone knows already, they may be put in a spot of vulnerability where they may feel they have to prove their worth more than a regular kit, not just because they are half-Clan, but because everyone likes being afraid of Tigerstar's bloodline.
Jay, Lion, Holly, Misty and Stone were already shown to be assets to their clan so they never felt too much pressure for being the product of forbidden love from their clanmates. How they felt personally about the information varies with each character.