Is it possible to obtain "liked" status (the one you need to get into the safehouse). Without finishing "Render Unto Caesar?"

I did odd jobs for Vulpes Incultas but I'm only at Accepted. Anything else?

Sell NCR dogtags to Cottonwood Coves commanding officer(I can't remember his name). About 20 will jump you up to Liked from Neutral, IIRC.

Well I know of the dogtags. How can I take out NCR troops without it affecting my status with them? If I wear legion armor will that negate it?

Do Vulpes quests. (Doesn't lose NCR rep)
Do the quest for Lucius.
Fight in the Arena.
Complete Eye for an Eye by betraying the NCR (doesn't lose NCR rep)
Several NCR corpses can be found that might have dog tags (Nipton has a building filled with NCR soldiers, sometimes dead soldiers are found south of Forlorn hope). Turn in the dog tags one at a time for maximum rep.

Does winning in the arena affect your reputation? And I think Lucius has a quest.

Also sniper NCR guys from a far distance.

Hanging around Searchlight surroundings/Legion raid camp gave me about 8 dogtags as Legion and NCR patrols fought and Legion won, always. Corpses in Nipton, Forlorn Hope and Camp Guardian also yield a mighty fine bounty of dog tags(at least combined, that is).

I've always had Legion patrols lose ever since service rifles got upgraded. Is your game modded?

I heard if you sell your tags one by one, you get more rep than if you sold them all together.

I got liked status by repairing the Howitzer in the Fort and by well, telling this one guy in Cottoncove over and over how to disarm mines! LOL