If you heat them past the smoke point, yes, they lose a ton of nutrients and become quite unhealthy. In normal use, no, not really. The impact of heating them is quite small. And comparing them to animal fats...they're clearly slightly better in some ways, but slightly worse in others. How you balance those factors...I don't think we remotely have good data on yet.

For now I'd just try and eat in moderation and look askance at people making sweeping assertions about any food being all good or all bad.

(On the other hand, we have much better data about the environmental impact of vegetable versus anaimal calories.)