Yeah, it’s a good idea to complete them all, they all give out equipment and stuff to help you get started.
Eventually if you continue doing missions, you’ll gain standings with some Factions while at the same time incur bad standings with other Factions. It’s just how the system works. The best thing to do is decline missions that are against other Empire Factions and just accept missions against Pirate Factions. Unless of course you don’t care about it and prefer to be a loyalist.
Anyway, just in case you find yourself in that position, you can check out ‘The Plan’ to help resolve that issue: