The current method of getting rep has nothing to do with sense. You can do bad things and then pay it back by doing good things.
This suggestion tries to gear the reputation so that good rep actually means you have done something for the community and its members. I'll keep this as short as possible, further info will be provided by request.
Each faction has a quartersmaster that hands out free munitions, sets of stuff to all members twice in a real world week. The items depend on your rank. The overall item quality depends on faction wealth.
You can raise your rank by checking in the quartermaster and showing you haven't lost your gear. You can also raise your rank by providing services to the faction.
Services are giving certain items, crafted - not farmed. Or doing special "profesion service". This means that you go to the quartersmaster and offer your help. Your crafting cooldown rises by 2hours and your faction receives profesional service points depending on your profesion. These service points are usable by all members for free and they are divedid in doctoring, repairing or upgrading. So if someone has broken metal armor, he can go to the quartermaster and have his armor repaired, but it reduces the faction's pool of profesion points. Profesion points represent that your char has worked for hours in the faction's factories or hospitals. But instead of actually doing it, the action only exists as cooldown and dialogue. Non-members have to pay for these services, which raises faction's wealth.
When you give items like raw materials and top tier gear, you raise your rank but you also raise your faction's wealth. Faction's wealth determines how good the weekly free munitions are for everyone. Even if you got highest rank but your faction is poor, you'd end up just having 2nd tier equipment while if it was rich, you'd get 3rd tier stuff. TC town products like gold and uranium could give faction rep aswell and raise the faction's wealth.
Selling crap and first aiding locals no longer gives rep since it doesn't help anyone.
If you spend too much profesional points and constantly lose gear, the guartermaster denies your access to them until you have paid them back by working.
Attacking and killing fellow members should have irreversible consequences and permanent loss of rank&rep. All members are automatically greentagged.