Yes, it is legal for the DM to give you e.g. CR 0 creatures, but unless it was explicitly house-ruled or for in-universe reasons, it would go against the intent and spirit of the game to do so.
Here's a framing I think is helpful: when your character casts conjure animals, and the GM is deciding what creatures are summoned, the GM is essentially playing the role of the pseudo-character "the in-universe source of your character's magic." For Druids and Rangers, the classes with normal access to conjure animals, that source is approximately "nature." It can totally make sense that the in-universe forces of nature can't provide you with the exact wacky creature you picked out of the Monster Manual. An allosaurus is a beast with CR 2, but it may not make sense in-universe to summon one; the universe you're playing in might not have had dinosaurs, or have handy access to some to summon because they've all been dead for umpty million years.
There may be clear in universe reasons the source of your magic is unwilling or unable to be helpful. If you were a warlock, perhaps your patron is angry with you. If you're a druid, you may be in a metropolis where the forces of nature don't have much sway. But such an issue should certainly be an actual plot point.
Alternately, the DM may decide that conjure animals is, in general, unbalanced, and decide to nerf it in some way as a house-rule. It would be uncool for them not to tell you about that, but that's a valid thing a DM may need to do for some spells.
But unless there is some clear reason otherwise, the source of D&D characters' magic goes along with what they're trying to do. A character is trying to summon animal allies with a certain rough power level, and the spell as implemented should do that. Maybe not giving them exactly what they want, but certainly not actively undermining them, unless there's a clear story reason.
I'd put it this way: the choice of what animals are summoned is put in the DM's hands because the summoned creatures need to make sense in universe, and the DM is the assigned arbiter of that decision. It's not put in the DM's hands as a weapon to use against players.