Should I abandon my Relic Quest?

So the question here is should I abandon the relic for my monk and just go ahead and get the warrior one?

Not sure anyone can really answer that but you.

If you abandon your relic quest you'll have to start it all over again (including getting the weapon/melding the materia to it).

If you haven't got that far and/or you really don't care then reset probably isn't a bad thing, but otherwise that's for you to decide how far you've got and how beneficial it'd be to you to have a relic for whatever job.

Whosever your main

As a monk/warrior player that got relic for both jobs, I would say stick with monk till you get relic then do warrior. Problem with warrior's relic quest is you need good gears on him and good players that trusts you at tanking to do Titan HM. It's a lot easier getting into a Titan HM PUG as a monk than as a warrior.

depends on how far you are into relic.

if you are at primals, don't bother abandoning it. if you aren't, its up to you.

its easier to just see it to the end (and less time consuming too)

Stick with monk first. As lemon already said, it's easier to get into a group for titan than it is for a warrior. Warriors have it really bad against titan unless you yourself are well geared and have very geared healers in your group. I'm currently trying to beat titan as a warrior dps for my relic with a paladin main tanking