Subtitles are working fine for me! This may be a personal issue with your game. Try removing the subtitles then put them back on maybe,
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I have tried turning them off then back on. It does not fix the problem. I have a friend who is having the same problem as well. It's already created problems for me on patrol. I hate to think what TTK will be like...If you know anyone else having this problem please encourage them to report it. I'm afraid Bungie will not prioritize accessibility like this unless a lot of players are having a problem with it.