Can I get new characters or do mystery portal if I don't have Xbox live gold

Because all Mystery Portal events involve either Multiplayer or online Co-Op if you are playing through an XBox or a PS4 you'd need a subscription to be able to participate fully. Without a subscription you aren't allowed access to the multiplayer or online Co-Op experience so that's a huge hurdle to obtaining the new Character Classes in any reasonable amount of time.

The only way to earn Rainbow Stars in "Offline" mode is to earn regular Stars and then exchange them with the Seagull in Town Hall at the rate of 7 Stars for one Rainbow Star. Because of the exchange rate it means you'll need to earn 350 regular Stars to exchange enough to earn the 50 Rainbow Stars necessary to have a "No Guarantees Whatsoever" chance at a Trial Key every two or three months due to the hard cap of 200 regular Stars depending on whether or not you clear your Plant and Zombie Quests every time the board refreshes and how often you receive and complete an Epic level Quest.

So the short answer is, Yes "offline" players can get access to the new Classes but you'll be waiting an incredibly long time.even with perfect luck receiving Keys.