Multi-Account-Containers has the ability to "Always Open This Site In..." and lets you select a container. However, I use the default "no container" for almost everything and only use containers for certain tasks. I would love for certain sites to always open in the "no container", but there is currently no way. Other container features allow selecting the "no container" container.
At best if I am in a container, I can open a new tab, go to the site, and then "Open in New Container Tab: no container" ... but at this point I've already opened the tab in the old container. The only other solution is to switch back to the default non-container and swap tabs a few times to make sure the "current container" sticks when opening a new tab.