Why can't I eat at vegan restaurants and order salad only?

You cannot eat salad at vegan restaurants, even if they don't serve meat, because there are serious kashrut problems with the vegetables themselves. This is something many people don't understand - they think kashrut is only about meat, but the vegetables have major issues too. When you eat at a non-kosher place, even if it's vegan, the vegetables are not properly cleaned according to Jewish law. The goyim are not obligated to wash vegetables the way we are obligated to wash them. We have to wash vegetables multiple times with salt and soap to remove all the bugs - the worms, maggots, flies, spiders, and other insects that are naturally on vegetables. If you eat one bug, it's six different sins from the Torah. That's actually worse than eating pig, which is only one sin. So when you eat a salad at a non-kosher restaurant, you're almost guaranteed to be eating bugs, and you're committing multiple violations - sometimes worse than eating treif meat. The cleaning process for vegetables in a kosher establishment is completely different from what they do in non-kosher places. They wash superficially - just enough to make it look clean. We wash with salt, with cleaning agents, multiple times, checking carefully. It's like a science project just to prepare a proper salad. Some fool who calls himself a rabbi wrote that you can go to any vegan restaurant even without a hechsher, saying if you can't see the bugs, don't worry about it. This is completely wrong and against halacha. He created a new law that doesn't exist. Don't listen to such people. Bottom line: if it doesn't have a proper kosher certification, you cannot eat there. Period. The vegetables need to be kosher just like the meat needs to be kosher.