Kiwi and strawberries can spark the same allergic reaction, but you won't know till you try, iyswim! I think at six months they reckon they're fine, it's if you wean at four months you need to be careful.
I think they recommend putting a tiny amount of kiwi/strawberry on the lips to check for allergic reactions, any swelling etc then steer clear!
If you have allergies yourself pbk then you should be a bit more cautious, but if there's no reason to anticipate a problem then yes, egg white is fine. If you have an aversion to it yourself then I would perhaps leave it til a bit later, and offer without any other new foods, so that you can be sure it is the egg if it does cause a reaction.