I prefer the "play your way" strategy. Here are the key points:
- Screw what everyone else is doing
- Do what you want
- Help yourself
- Don't get upset when people aren't doing what you want them to do
- Don't act too shocked when people don't like what you're doing
This is the best way to play Destiny if you're not playing with friends. If you want to speedrun strikes, do that, but be prepared to have to carry out half of the strike on your own.
If your fireteam wants to speedrun but you want to mop up aliens, let them go ahead and do their thing. Shooting ads is fun.
If you're serious about completing strikes in record time, you'd be serious enough to either not need the help of randos or you'd bring your own team.
If people don't make the Public Event heroic, then who cares, the loot isn't significant enough to send them hate mail.
Have fun and mind your own business...