Prior to this commit, the `HttpEntityMethodProcessor` would check HTTP
conditions on non-safe requests (i.e. not GET/HEAD). This would prevent
Controllers from returning `ResponseEntity` containing response headers
with updated values of `"Last-Modified"` or `ETag` once the resource has
been updated.
This commit avoids those checks for non GET/HEAD requests - this code
can still be leveraged from Controllers themselves using
`ServletWebRequest::checkNotModified` methods.
Issue: SPR-15780
ed7684d2b2