I’d say yes, they could prohibit you from open carrying throughout the common areas. However, what you do within your apartment is your business (within reason).
You have a reasonable expectation of use and enjoyment of common areas, i.e., passage, use of community BBQ, laundry facilities, parking areas, etc. However, other tenants also have this same reasonable expectation of use and enjoyment.
If by your open carrying causes others occupants fear and feel their right of enjoyment is diminished by your actions, the property owner could construe this as causing harm, i.e., other tenants threaten to move, repeated calls to law enforcement (man with a gun), discouraging prospective new tenants, etc. In short you could be severed with a notice to quit.
The property owner could amend the contract addendum (Facility Rules) prohibiting said activity with a 30 day notice of change to the rules. If your on a month to month, I believe they could hand you a 30 day notice requesting you vacate…No cause needed other than they just don’t want to do business with you anymore.