Will the mass of the earth be greater or lesser 100 million years from now. Ignoring outside factors such as meteors and satellites?

But the outside factors are the answer to the question.

Earth would gain mass by meteors and lose mass by satellite launches or any other "outside factor".

One cannot address changes to a closed system when it's not a closed system.

Answer depends on how you define "such as". No change in mass can occur in a perfectly closed system. Ionizing radiation will convert back to matter, increasing the mass of Earth a few parts per google per day. That is because the mass of radio active isotopes has been decreasing for trillions of days, except the few days that humans have exploded H bombs. With any definition the mass change is extremely small, and thus debatable.

I'm not sure how you can ignore meteors... they add tons of material daily to our planet. We tend to lose a bit of our atmosphere due to solar wind, but that's also an outside factor. I would guess we'd lose mass - ignoring the above...

Slightly smaller, since radioactive decay will transform some mass into radiation. That is, of course, if you don't consider that an "outside factor". Trees and plants don't produce mass; they are made from matter that was already there.

I always thought trees and plants growing and then dying would make the earth weigh more over time.

The same