It is not willy-nilly nor is there much doubt in the legality.
There are morality clauses in NHL contracts that cover things like this.
If there was not a morality clause and the team terminated the contract because they disagreed with his morals, Leipsic, and by extension your arguments/concerns would have a clearer path to counteraction, but it's explicitly written in, and Leipsic knows that and signed to it when he signed his contract. The League even approved it too; you can't just send any contract to termination, which means it must have been vetted against some by-laws (or it was mutually agreed upon, in which case all of this would be moot anyway).
The NHLPA may file a grievance internally, just for due process, but I doubt if there are any external litigations it will be about the termination.
Additionally, there is not real reason why the team would have to say consistent, as it were (other than court of public opinion). It is up to a team when they want to invoke such clauses.
Lastly, in terms of honouring the contract, Leipsic had no more contract left. He was an impending RFA and the last pay cheque had already been resolved so there was no money left owing either (if plays does resume, admittedly, he could have in theory still played, though, yes).
If Washington, then, had made their decision to part from already and not re-sign him, they then really had 3 choices:
1) terminate him now (either with the player's agreement or invoking a morality clause)
2) not entering club-elected arbitration or offering a qualifying offer, thus letting him become an unrestricted free agent mid-June (dates are a little subject to what happens with the draft)
3) offer him a qualifying offer (at the risk him accepting the offer or electing for player-elected arbitration and being stuck with him) and retain his rights but not sign him, effectively holding him hostage from the NHL and any League with a transfer agreement
Option 3) is just bad for many reasons.
Option 2), it might be the path of least resistance, but it just prolongs the process and makes the Capitals look non-committal in the court of public opinion by not just sitting on it
Option 1) is clear, direct, legal, and if grieved they can easily point to options 2&3 and claim they were actually doing him a favour by not holding him for longer, allowing him to begin his own process of reconciliation and finding new work