A quality build character will likely focus on direct weapon damage since a majority of weapons in the game scale primarily from either strength or skill. A great weapon for a quality build is Ludwig's Holy Blade since it scales from both strength and skill with a B.
Bloodtinge governs damage from firearms (and some weapons). Firearms usually deal low damage, but can be extremely effective and deadly in the hands of a high bloodtinge character, especially if combined with Bone Marrow Ash. A quality build will likely lack in this area, so firearms will not be a primary source of damage for them, though they will still be effective for setting up gun parries.
Arcane influences quite a few things. The first is drop rate; increasing arcane also increases item drop rate, so ignoring this stat may make it difficult to replenish your item stores later in the game. Additionally, some items which deal damage, hunter's tools, and sprayer sidearms (like the Flamesprayer) scale from arcane. Without high arcane, you shouldn't expect a high amount of damage from this equipment. Finally, arcane influences damage dealt by elemental effects. Non-arcane builds will still deal additional damage from such buffs, but not as much as someone focused in arcane might.
In general, the main source of damage for a quality build will be weapon damage. Neglecting bloodtinge or arcane will cause you to miss out on their benefits noted above, but you can easily invest in other stats as well as strength and skill if wish to remain well rounded.
You can get more information on stats here as to how their values might affect scaling.