Maybe you're wrong about reading those two stories in the same anthology.
Starpilotsix seens to have identified the first story as "Dreams Are Sacred" by Peter Phillips. That story was first published in Astounding Science Fiction, September 1948, which is available at the Internet Archive.
The second story sounds like "Unready to Wear", a short story by Kurt Vonnegut, Jr., which was also the answer to the old question Short story about people achieving enlightenment living forever with disembodied minds. Here is the ISFDB synopsis:
A part of humanity has become "amphibious" which means they are able to leave their bodies at will. They have a reserve of very healthy and good looking bodies which can be used at will, but most of their time they spent as incorporeal happy beings. Those humans who haven't left their bodies consider them deserters.
This story was first published in Galaxy Science Fiction, April 1953, also available at the Internet Archive. You might have read it in The Second Galaxy Reader of Science Fiction or in a Vonnegut collection, either Canary in a Cat House or Welcome to the Monkey House. However, if "Dreams Are Sacred" and "Unready to Wear" have appeared in the same anthology, the ISFDB doesn't know about it.
The second story involved man evolving to a higher form of consciousness by "stepping outside" of his corporeal reality into a non physical spiritual reality.
By following the instructions in Konigwasser's book for about two years, almost anybody could get out of his body whenever he wanted to. The first step was to understand what a parasite and dictator the body was most of the time, then to separate what the body wanted or didn't want from what you yourself—your psyche—wanted or didn't want. Then, by concentrating on what you wanted, and ignoring as much as possible what the body wanted beyond plain maintenance, you made your psyche demand its right and become self-sufficient.
That's what Konigswasser had done without realizing it, until he and his body had parted company in the park, with his psyche going to watch the lions eat, and with his body wandering out of control into the lagoon.
The final trick of separation, once your psyche grew independent enough, was to start your body walking in some direction and suddenly take your psyche off in another direction. You couldn't do it standing still, for some reason—you had to walk.
There was opposition from those who felt that losing their physical self was a loss of their individuality.
That's why I can't get sore at the enemy, the people who are against the amphibians. They never get out of their bodies and won't try to learn. They don't want anybody else to do it, either, and they'd like to make the amphibians get back into bodies and stay in them.
Why I liked the story was that our hero who narrated the tale was keen to persuade the unbelievers because the new life was so much better.
"Then you despise human beings and everything they do," he said.
"I like them fine—better than I ever did before. I just think it's a dirty shame what they have to do to take care of their bodies. You ought to get amphibious and see how happy people can be when they don't have to worry about where their body's next meal is coming from, or how to keep it from freezing in the wintertime, or what's going to happen to them when their body wears out."