Dedicated Minecraft server that's Xbox accessible
Solution 1:
Currently, considering Vanilla versions¹, it is not possible.
There are different Minecraft versions as people pointed out on the comments. The only available version for Xbox (Either 360 or one) is the Bedrock edition, while for Linux, the only available version is the Java one.
¹I cannot guarantee that there isn't a modification that either allows the Bedrock edition to be played on Linux or emulates the Java on Xbox. I at least know none nor saw any mention of it.