Before i describe this, please don't ban me for this bungie xD
It really wasn't intentional.
I was doing playlist strikes and the 3rd one happend to be a DLC strike called The Scarlet Keep.
Never had that one before but when i finished that strike i was still on the Moon's orbit so i decided to click on the Moon from the Destinations tab to see what would happend and it showed my ship going to the Moon and then 2 cutscenes started playing.
The first one was Eris Morn in a cave meeting some red ghost and the second was my ship landing and the Moon being under attack.
After the cutscenes it started the Shadowkeep Campaign which i completed (and enjoyed xD) and i was then thrown out to the orbit again.
I clicked the Moon again to see what would happend and i just went there just like that.
And now i have access to the Moon.
I can't do any bounties and some things are still locked but i can do patrols and public events.
If this was supposed to happend then sorry for making fool out of myself but if not please no ban ok? :D
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The moon is open as a patrol space to everyone. You need Shadowkeep to do the actual campaign.