Are modern birds reptiles?
Yes and no. Sorry.
If you mean are they reptiles in terms of descending from the original reptiles then yes! But now they're in a specific group, aves and we group other reptiles as a just reptiles.
So going by lineage yeah, they are not only reptiles they are dinosaurs. Going by physiology, their different, not reptiles,
It's like how rock music was all soft rock and then you eventually got, like heavy metal and death metal. Did it come from rock music? Yeah. Is it in the rock section? Yeah. Is it the same to like, Elton John. No.
Ancestrally: Yes, definitely.
Physiologically: No scales, not quadruped, worm blooded. Can fly. No.
So technically yes.
No Birds are not reptiles.
The Darwinian theory of descent with modification postulates that all organisms are products of common descent from ancestors.
Using this theory the most likely source of a common ancestor for birds was a ground living dinosaur. The general consensus of scientists presently is that birds "evolve" from dinosaurs.
The is a great lack of empirical evidence for the theory that birds evolved from dinosaurs. However there is some evidence such as the Archaeopteryx. The relationship between dinosaurs and birds are still open to debate. Yet Dinosaurs are the most likely candidate for a common ancestor of birds.
If the theory that birds came from dinosaurs birds is true birds are still not presently dinosaurs or reptiles. Birds are warm blooded dinosaurs and reptiles are cold blooded. Birds have feathers, reptiles have scales. Both lay eggs, that have a hard shell. Birds have light hallow bones, while dinosaurs and reptiles have heavy solid bones.
Birds may or may not have evolved from dinosaurs, however birds are not presently reptiles.