Why are women Pasul leEidus ?
Does this still apply?
וְעָמְדוּ שְׁנֵי-הָאֲנָשִׁים אֲשֶׁר-לָהֶם הָרִיב לִפְנֵי יְהוָה לִפְנֵי הַכֹּהֲנִים וְהַשֹּׁפְטִים אֲשֶׁר יִהְיוּ בַּיָּמִים הָהֵם.
And they shall stand the two men, who have them the conflict, before God. Before the priests, and the judges, that will be, in those days.
Three different approaches are taken:
As this is derived as a biblical fact, it would always apply2.
1. This is a device known as a gezerah shavah
2. Note that there are areas of law for which womens' testimony is accepted: "...Women are admitted as competent witnesses in matters within their particular knowledge, for example, on customs or events in places frequented only by women (Rema ḤM 35:14; Darkhei Moshe ḤM 35, n. 3; Beit Yosef, ibid., n. 15; Terumat ha-Deshen Resp. no. 353); in matters of their own and other women's purity (Ket. 72a; Ket 2:6); for purposes of identification, especially of other women (Yev. 39b); or in matters outside the realm of strict law (BK 114b). In post-talmudic times, the evidence of women was often admitted where there were no other witnesses available (cf. e.g., Resp. Maharam of Rothenburg, ed. Prague, no. 920; Resp. Maharik no. 179), or in matters not considered important enough to bother male witnesses (Resp. Maharik no. 190; Sefer Kol Bo no. 116)."
Loosely translated from Kipa.co.il
Women are disqualified because of a gezeirat haKatuv, [an inference from the Biblical text], as the Rambam says in Hilchot Eidut 9:2, based on Devarim 16:6 and 19:15, where it uses the male gender, and not the female. Thus we see that women are not disqualified because of their competency or trustworthiness, rather because of a biblical verse.
In addition, women are disqualified due to their honor\respect. A court does not have the right to subpoena women and subject them to interrogation. The flipside is that women are disqualified to testify, since they cannot be subjected to this disrepectful public appearance. In fact, in cases where the courts seek the testimony of women, messengers are sent to her home to perform the questioning, out of respect.
However, women are qualified to testify in certain cases [see article for details].
The Sefer Hachinuch addresses this in two places.
Mitzvah # 37:
ונוהגת בכל מקום ובכל זמן בזכרים אבל לא בנקבות שאין הנשים בתורת עדות שהעדות צריך כיוון וישוב הדעת הרבה
And this is applicable in all places and at all times, for males but not for females because women are not included in the laws of testimony since testimony requires much focus and equanimity.
Mitzvah # 122
ונוהגת בכל מקום ובכל זמן בזכרים אבל לא בנשים שאין הנשים בתורת עדות לקלות דעתן
And this is applicable in all places and at all times, for males but not for females because women are not included in the laws of testimony due to the lightness of their intellects.
The Midrash Aggada also relates the reason to a feminine flaw.
ותכחש שרה לאמר. מכאן שהנשים כחשניות הן מפני הפחד ולכך פסלן הקב"ה מלהעיד עדות
And Sarah denied, saying. From here [we see] that women are deniers out of fear, and therefore the Holy One Blessed be He invalidated them from bearing testimony.
I once heard an explanation of this halacha from Rabbi Orlofsky, in which it has nothing to do with women's competence or lack there of, and never implied a former lack of competence (as your question does).
Women are created with a stronger emotional sense, and are meant to be that way. They are meant to be in touch with their emotional side and not stifle it. This is why women are generally more compassionate (Megillah 14b), and they are meant to be.
Therefore, women are excluded from certain things that depend on stifling one's emotional attachment. One example is Rabbanus, where a Rav is meant to decide a psak based on a cold calculation of what is the correct halacha and not bend the halacha based on sympathy (sometimes the halacha itself may lend itself to leniency depending on the circumstances of the individual, but the point here is extra-halachic leniencies based on feelings of compassion) - it is unhealthy for a woman to force herself on such a consistent basis to suppress this part of her. Another example is witnesses - one is required to give testimony that will put someone to death, no matter how difficult of a situation it was for the person - it is forbidden to withhold testimony if you have it. It is therefore an exception for the sake of women to not be bound to such a thing.
the first comment on the OP from @user4523 says brings the Ben Ish Chay's answer to your question
from where it seems, in short, the main reason is that woman should stay at home and not be with men (since it might lead to promiscuity)
if her testimony would be believed some woman would use it as an excuse for promiscuity (like saying that she was in privet with 3 men because she was giving testimony)
another reason is that this is part of the punishment (curse) for eating from the tree of knowledge
Pirkay D'rabbi Eliyeser 14.5
Hashem gave the woman nine curses and death:
1. the afflictions of child birth
2. afflictions of blood of virginity
3. the affliction of pregnancy
4. the affliction of bringing up children;
5. her head is covered like a mourner,
6. and she does not shave it except on account of immorality,
7. her ear is pierced like (the ears of) perpetual slaves;
8. like a hand-maid (slave) she waits upon her husband
9. she is not believed as a witness
and after all these, death.