Do you think the "Bless" spell would work on an unwilling target? Why or why not?
Do you think the "Bless" spell would work on a target who is hostile to the cleric's god? Why or why not?
Do you think the "Bless" spell would work on a target who personally dislikes or disrespects the cleric? Why or why not?
When you ask "why or why not?" are you asking about the mechanics or the fiction.
By the mechanics, it works on an unwilling target regardless of attitude towards the cleric or the cleric's god. Given that the spell is an Enchantment, the most natural explanation for this, in the fiction, is that the spell controls the mind and emotions of the target. (Though it is odd that this would be one of the few mind-control spells in the game that does not permit a saving throw.)
Personally I think that makes for a very weak fiction that is completely divorced from the archetype that the cleric is meant to be expressing: in tales of holy knights, and fighting under relics of the True Cross, etc, it is not
mind control that makes the soldiers fight harder, but
inspiration and
religious devotion and the presence of
divine grace.
In 4e clerics have a healing ability called Healing Word, which allows the recipient to expend a surge to regain hit points. It seems to me obvious that when a cleric speaks a healing word, s/he is not using magic to reknit bones and close wounds (that's what the various Cure . . . Wound spells are for). Rather, s/he is infusing herself with divine grace which then lifts the spirits and martial resolve of the recipient character (and perhaps the grace flows into the recipient - there's plenty of room for interpretive flexibility).
I have always thought of the Bless spell in the same way - the cleric performs a ritual which inspires the recipients and infuses them with grace and valour. (3E formalises this by making the bonus a Morale bonus.)
What happens if the cleric tries to use Healing Word, or Bless, on an apostate? In my view the game rules don't cover this - it's the sort of corner case they're not concerned with. In classic dungeon-delving D&D I think the notion of a character being an apostate isn't really on the table - we take for granted that the PCs are happy to receive the blessings of the divine which their cleric companions call down upon them.
In more "roleplaying"- or "story"-oriented games, the possibility becomes a live one, but I think it is left for the table to sort out. If the table wants to just handwave it away as "m
aaagic" or mind control that doesn't allow a save, I guess they can. What I find puzzling is that a table would be happy to handwave that away, but want to drill down super-deep into the mechanical and motivational logic of a warlord. It seems to me that a player who is really concerned about the implications, in the fiction, of a warlord being able to inspire his/her PC is likely to be equally worried about the implications, in the fiction, of a cleric being able to mind control his PC with a 1st level spell that doesn't allow a saving throw. And the obvious solution would be to allow a save vs Bless for apostates, or even rewrite its targeting to only affect willing allies; and a warlord could be handled the same way.
My reading of the 5e PHB seems to differ from yours.
Page 6 of the Basic PDF says that:
Class broadly describes a character’s vocation, what special talents he or she possesses, and the tactics he or she is most likely to employ when exploring a dungeon, fighting monsters, or engaging in a tense negotiation.
The game clearly allows that swearing a pact with a devil is a
vocation that is distinct from being a great thief, or a fierce warrior. Similarly for being beloved by the gods, or for being born of dragons, or for being able to sing the music of creation.
There is no a priori reason in the fiction why this should be so. In Nordic, Celtic and Finish legend there are fierce warriors who are also able to sing the music of creation. There a folk tales of great thieves making pacts with the devil (which, in some cases, might even help explain their success as thieves). Someone who wrote a story about a dragon-blooded hero who was the fiercest of all warriors and also able to shoot blasts of fire and fly on magical wings wouldn't be making some sort of category error.
But in 5e (as in other versions of D&D) these various abilities are silo-ed off. Not for reasons to do with in-fiction truths, but for reasons to do with making a playable, class-based game. Making a warlord a unique class is doing the same thing: it is opening up the possibility of a character whose
vocation is being an inspiring hero; and the result is that characters of other classes won't be as inspiring as that hero is (though they may still be inspiring in mechanically lesser ways). Much like a fighter who swears a pact with Cthulhu - whatever the benefits of that pact, in most 5e games the player won't be allowed to mechanically gestalt his/her fighter with warlock.
That's how a class-based game works.
EDIT: It's obvious that a FRPG need not be class-based, and hence that the mechanics of character-building need not erect barriers between (say) sword-fighting and spell-casting (so long, Gandalf) or between being empowered by the blood of a dragon and being a heroic warrior, which from the point of view of the fiction are completely artificial.
Runequest is probably the best-known game that illustrates this point.
But D&D is not such a game. It uses classes. That means that capabilities and traits are silo-ed by the mechanics. The fiction either has to bend to that, or (as is more often the case) just politely ignore it.