Does turning off engine at red lights save gasoline?

It saves an amount too small to measure, but IMHO it truely is not worth the added wear on the starting system. McP correctly pointed out that hybrids do this, but their starters are designed to survive routine cyling to a greater extent than yours is.

But unless you live in an urban area, where slow starting from a light can earn you a crowbar on the skull, it isn’t dangerous. Much of the difference in the responses you’ll get is truely philosophical. Some feel that every drop saved is important, some do not. I’m in the latter group.