Breaker connection on common neutral situation
No.  The two black/red wires that share a neutral are part of the same circuit, and the formal name is a multi-wire branch circuit (MWBC).  either 


the two breakers need to be fitted with a listed handle-tie for that breaker type, which as a side-effect will force them to be on opposite poles; or 
the two breakers need to be replaced with a 2-pole (240V) breaker of a correct type for that panel.  By nature a 2-pole breaker puts its 2 lugs on opposite poles.  


The 2-pole breaker may be of GFCI, AFCI or GFCI+AFCI type.  If so, it will confer protection to the entire MWBC.  



Listed, correct handle-ties can be annoyingly hard to find, so in most cases just use 2-pole breakers which are available everywhere.   

A double-stuff/duplex/tandem/twin breaker is not a 2-pole breaker and the essential clue is that the handles are not tied and cannot be tied. 

The purpose of handle-tying is to assure common maintenance shutoff.  It is not essential for MWBC breakers to be common trip, but using a 2-pole breaker will have that effect too. 

If you are stuck with a crowded panel using double-stuff breakers, then handle ties are usually not an option.  Go with quadplex breakers instead.