Is it normal for the RTE to be almost 80 percent different from the TMI it was generated from?

This could be normal, but it depends on how the difference is being measured. The RTE (reduction to the equator) significantly alters the shape of the anomalies, so it shouldn't resemble the TMI. Even so, an 80% difference warrants a quick review to rule out calculation or parameter errors.

It changes the shape of the anomaly. The filter transforms anomalies into what they would look like with a horizontal field (0° tilt). At the equator, a body with induced magnetization produces a low centered on it, with smaller highs to the north and south. In the TMI at mid- or low-latitudes, the anomaly is usually a displaced high-low pair. Compared point by point, both grids can appear very different, even though both are correct.

It attenuates north-south trending structures. At the magnetic equator, features aligned with magnetic north generate almost no anomaly. The RTE weakens them and preserves or enhances east-west features, which significantly redistributes the map's energy.

How to verify it
Measure the difference carefully. Compare the residual anomaly (without IGRF and without a mean level) against the RTE. Use the correlation coefficient and a visual analysis of the shapes, not the percentage difference in values.
Visual review. Over known or obvious magnetic bodies, the RTE should show centered lows aligned E-W. If it shows centered highs or unusual shapes, suspect the parameters.
Test with a synthetic model. Generate the anomaly of a prism or dipole with the survey's inclination and declination, apply the same filter, and verify that it produces the expected theoretical result.

Likewise, you should try RTP and RTE, choose the best one.

Gus.