You can open custom tab links in a new tab in Chrome 58, as it was recently discovered that the Dev channel version of Chrome 58 for Android now allows this action. Chrome Custom Tabs previously only had the ability to open up links in the same exact tab which meant that you would have to move away from whatever was on the currently opened tab you were browsing, but no longer. While this is still only available in the Dev Channel version of the Android app, which means it will still have to go through the Beta Channel before it makes it to the stable version of Chrome for Android, it'll certainly make things smoother once it gets to that point.
Chrome Custom Tabs provide a number of different benefits for developers and for users. Custom tabs make it easy for developers to add a touch of customization to the tab like colors for the toolbar, exit and enter animations, and they can load up faster as they allow developers to make it so that content pre-loads on the page when choosing to open content in a Chrome Custom Tab.
For those using the Dev Channel version of Chrome 58, now when opening up a custom tab link, long pressing that link will pop up the option to open it in a new tab alongside the other available options, and you'll be able to keep the currently opened tab right where it is which means you can flip back and forth between the new tab and the tab you're on, which should be especially useful if you're not finished reading or browsing on that tab. This new change is also available in the Chrome Canary version of Chrome for Android so if you're using that instead of Chrome Dev you can test it out there too, although it is worth noting that Chrome Canary is a more experimental version of Chrome than the Dev Channel version so if you're not using either and were going to give one of them a shot, the Dev Channel version might be a better option. At the moment there is no indication of when this might make its way into the Beta and stable channels.