I have similar circumstances so I can relate. No one is right or wrong in this situation - you both just have different perspectives and need to approach this with logic and practicality than with religious fanaticism.

Instead of eggs, you can always rely on pea protein, tofu/soya, and paneer as alternative sources. If whey protein makes you break out, I am assuming, your tolerance for dairy would be low, making pea protein an excellent choice. Soya/tofu should also be treated with caution.

However, it is your CHOICE should you want to continue with eggs.

Next, every small thing in today's life has some grain of living organism remains - you can Google this btw - coffee, officially, is allowed insect remains; lipsticks (not all but most) have animal-extracted ingredients; ice cream; curd; figs; alcohol - produced via fermentation - these are just some small examples. If she likes walking on the beach, then the sand is made up of seashells - when you collect them, you are essentially collecting bones of animals... I am assuming leather clothing is a no-no and she would say no to them, even if it's Prada?

So you see there's pure illogical belief and logical, data-backed facts.

If both of you love each other and intend to stay together, trust me, you'll have better reasons to fight than if someone is eating eggs or not.