If you have Spirit Guardians up protecting your party and your enemy casts Insect Plague to attack your group. Since it says that creatures are attacked when first entering the area, will all the Locusts die before they can bite you or your party? (this assumes the locusts only have a few hit points) Would this nullify the Insect Plague attack? Another concern is, if the ratio of locusts to spirits is high, say 50 locusts per 1 spirit (there is no count listed for either creature in spells description). Would the spirits be able to kill the locusts fast enough to stop them from attacking my party? (Perhaps the spirits us AOE damage?) Hopefully the insects get unsommoned when they die or it would be a slimy slippery mess on the floor afterward, which could be a movement hazard.
The insects from insect plague are a spell effect, and the spell clearly does not intend them to be treated as monsters (spells that do create items with stats clearly explain what they are and what the impact is of doing damage to them). Therefore, they are not stopped by damage to the swarm of any kind. In this regard they are similar to the Spirit Guardians and you could equally ask whether the insects kill the spirits - after all Insect Plague is a higher-level spell.
If it helps with scene description, you might consider that the spell continuously generates the swarm in its area for the duration, so that effects that could destroy small physical creatures are so fleeting as to not have any impact on the spell.
A way to use damage to stop Insect Plague is to break concentration of the caster.
No, Spirit Guardians does not negate Insect Plague
If the Insect Plague spell meant for the locusts summoned to be able to be destroyed by taking damage, stats would be given in the description, describing their HP, AC, resistances to various types of damage etc. Probably they would be given the stats of or similar to those of a Swarm of Insects as given in the MM. (Alternately, it might simply specify the type of creature it counts as, and/or state that "The DM has the creatures' statistics", as with the Conjure X spells.)
Instead, the spell says that the locusts remain for the duration of the spell, which is up to 10 minutes if the caster does not lose concentration. Thus we must assume that these are magical locusts, which cannot be damaged or destroyed, other than by breaking the caster's concentration.
We are getting into massive speculation here, but suffice to say that since these are magical effects and both the (potentially incorporeal) spirit guardians, as well as the temporarily summoned into existence locusts, are only there to serve the purpose of magical need and the moment concentration is lost on either spell they simply cease to exist; we can conclude that these are tied to the magic that summons them and thus not creatures with hit points.
These are both Conjuration Spells, and while Conjuration doesn't say they CAN'T be living breathing creatures with their own hit points, it does say the following:
Conjuration spells involve the transportation of objects and creatures from one location to another. Some spells summon creatures or objects to the caster’s side, whereas others allow the caster to teleport to another location. Some conjurations create objects or effects out of nothing.
No matter what they are, however, they are intrinsically tied in to the magic that summoned them forth. A magic spell such as Insect Plague, no matter what sort of creatures it is summoning, act precisely like a spell. It will take effect and afflict their targets with damage regardless of other spells in the area. Having another magical effect, a spell, that summons spirits doesn't interfere with the magic of Insect Plague. Only high level shielding magic can interfere with the effects of other spells.