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Yes, the bike should start in gear with the clutch disengaged (lever pulled in). Did you change clutch levers or switch to an aftermarket clutch lever prior to this happening?
There is a clutch safety switch inside the left housing that is activated by a tab on the clutch lever. Some aftermarket levers don't have the tab and cannot activate the switch.
My guess is the clutch safety switch is bad. The switch is part 72942-11 and costs about $25 +/-. It is a very easy repair.
It's not critical to leave your bike that way but, if you stall while moving, you would have to put it in neutral to start the bike instead of just pulling in the clutch.
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