These breakers appeared to be sharing a neutral, but it looks like they are on different legs.
If they share a neutral, they must be on different phases. They need to be on a tied double pole breaker of the appropriate rating.
Looks like there are opposite legs as you’ve mentioned. Chuck is correct about the handle tie requirement for MWBC’s but it didn’t enter the NEC until 2008 so pre-2008 did not require them.
Home was built in 1976, so I can only recommend they be tied together?
You may recommend anything you want to. It is just that they don’t have to do any of it.
If you explain it well enough, they buyer may do it on their own. 
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I see this often in mobile homes and short cut electrician jobs.
The install was correct back then when it was common to share neutrals between circuits for example a 14-3 NM cable feeding both kitchen lights and living room circuit. Homes that were wired before changes in code requirements occur, I usually just note it but don’t recommend anything be done. It’s the same with AFCI breakers.
I’d recommend that they be put on tied breakers. I just ran into this yesterday. “Code” may not have required it when it was done, but here in CO we are not code inspectors, we are safety inspectors. The potential of a homeowner wanting to replace an outlet and only turning off one of the circuits to do it is a real risk. MWBC’s are two separate parallel circuits with a common conductor. If the neutral is opened (i.e. an unsuspecting homeowner removes an outlet that doesn’t have the neutral pigtailed, but is using the outlet to continue the neutral path), the circuit on the other breaker will change to a 240 V circuit. Bad things will happen - frying everything that’s plugged into it and maybe even a fire.
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Yes these breaks are looks like that they are shared.
It is Single-Phase. There is only one phase.
The year in which the house was built is irrelevant. You can recommend anything that you want to recommend.