(some fundamentals of releasing & elevating hidden & trapped sparks)
Every convert who means to fully accept the yoke of Torah & all applicable mitzvot receives a new soul.
However, different levels of soul come according to the convert's level of intention.
Yet at the same time, sincere converts receive a special status with a direct lineage to Avraham Avinu & Sara Imeinu!
Furthermore, converts are subject to special protection, as commanded directly from the Torah and described in Tehillim 146:9, that Hashem guards & protects specifically the ger (even as He is, of course, the All-Powerful Shomer Yisrael).
We see that the great David HaMelech is the great-grandson of a convert (Ruth), and therefore Melech HaMashiach is also descended from a convert.
Rebbi Akiva was the son/grandson of converts & a direct descendent of the evil Sisera—yet he became one of Am Yisrael's greatest Sages.
So we see how wholly sincere conversion produces very special results.
The information in the above links, mostly gleaned from the great tzaddik Rav Levi Yitzchak Bender, explains why a truly kosher & sincere conversion is so powerful & so important for Am Yisrael.
After learning about the sparks & what conversion really does, both for the convert & for Am Yisrael, it's easy to deduce why invalid or questionable conversions are so damaging, not only practically, but also on a spiritual level.
Often, a potential convert contains a Jewish spark, which leads the soul toward conversion. Hashem planted that spark within because, for whatever reason, this person needed the process of conversion to carry out his or her soul rectification.
For example, some converts left Judaism in their former gilgul (lifetime).
To repair that terrible heresy, Hashem causes them to be born as non-Jews in a new gilgul — non-Jews who actively need to pursue Judaism & proactively adopt the full yoke of Torah & mitzvot to atone for the rejection they performed in their previous gilgul.
And that's just one interesting & newer reason. There are other better-known, all-encompassing reasons.
Regardless, it's vital that a conversion be carried out properly. The rabbis involved must be Orthodox—but being Orthodox isn't enough. These rabbis must also deal with conversion responsibly & take it very seriously.
The following short video contains a directive from the Lubavitcher Rebbe about how to conduct a kosher conversion & how to determine the sincerity of the potential convert. It contains wonderful direction & I wish every Orthodox rabbi would use this method when dealing with potential converts!: