The law of Chatzitza by male immersions:

Baal Keri: Men are not required to remove a Chatzitza from the body prior to immersion for the purpose of purification from Baal Keri, and so is the custom.[1] [Nevertheless some Poskim[2] are stringent.] However, this only applies if it is found on minority of the body, however a Chatziza on majority of the body is invalid even for a Baal Keri.[3] [Furthermore, some[4] write that initially one is to remove from the body all items that one normally removes upon bathing.]

Immersion of Teshuvah-Tosefes Taharah, Erev Shabbos: Despite the above, regarding the immersion of Erev Rosh Hashanah and Erev Yom Kippur [which is done also for the purpose of Teshuvah] one is to remove all Chatzitzas from the body.[5] Seemingly, this stringency of Erev Yom Kippur should apply also to the immersions of the rest of year, and Erev Shabbos and Yom Tov, for those that immerse for purposes of extra holiness, and not just Baal Keri.[6]

The law by clothing: In general, loose-fitting clothing is not considered a Chatzitzah by even a Biblical immersion.[7] Accordingly, men may certainly immerse while wearing loosely fit clothing such as a loose bathing suit, and tee shirt, and so should be done when immersing in public [i.e. public pool, ocean, sea], and it is unbefitting to be seen by others. Furthermore, even tight clothing, such as a tight bathing suit, is permitted for a male immersion when done for the sake of Baal Keri, as stated above that the laws of Chatzitza do not apply to a Baal Keri immersion. Nonetheless, initially and under permissible circumstances, it is proper for men to remove all their clothing prior to immersion, including even loosely fit clothing.[8]

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[1] Eshkol [Tefila 1]; Mamar Mordechai [1790] 1-2, brought in Shaareiy Teshuvah 88:1; Biur Halacha 88 “Vechen”; Shulchan Melachim in Halacha Lemoshe Dinei Tevilas Ezra 12; Piskeiy Teshuvos 88:8; Leaning opinion of Minchas Chinuch 180:4

Other Opinions: Some Poskim rule that a Chatzitza invalidates the immersion of a Baal Keri. [Amudei Eish Kuntrus Beis Tefila 12; opinion of Gadol brought in Minchas Chinuch 180:4] The Shaareiy Teshuvah ibid leaves this matter in question. The Ashel Avraham Tinyana [Butchach] 88 implies that initially one should remove a Chatzitza [The statement brought in Piskeiy Teshuvos ibid footnote 57 that the Ashel Avraham holds it does not even contain a Midas Chassidus is inaccurate] The Rashba [Yevamos 47] rules that a Chatzitza invalidates the immersion of a Baal Keri. Nevertheless, this only refers to one who needs to immerse Biblically, such as in the times of the Temple. However, for the immersion of Takanas Ezra even the Rashba agrees it is not necessary. [Shulchan Melachim ibid]

[2] See previous footnote “Other Poskim”

[3] Biur Halacha 88 “Vechin”; Halacha Lemoshe Dinei Tevilas Ezra 12, as is implied from the Eshkol

[4] Piskeiy Teshuvos 88:8; Vetzaruch Iyun on his source as the simple reading of the Poskim ibid do not imply that a differentiation exists between forms of Chatzitzas.

[5] Ben Ish Chaiy Netzavim 3; Kaf Hachaim 581:84; This is also required based on the teachings of the Arizal. [Kaf Hachaim 260:4]; M”E 606:8 regarding Erev Yom Kippur

[6] The above statement of the Poskim that validate the immersion of a man even if he has a Chatzitza refer specifically to one who is immersing due to being a Baal Keri. However, when immersing for Teshuvah purposes, as is done on Erev Yom Kippur, the Poskim ibid write that one is to remove all Chatzitzas. This arouses a question regarding those that are accustomed to immersing daily, irrelevant of being a Baal Keri, due to extra purity. Perhaps they too should be careful with all the laws of Chatzitza. Practically, the custom of Chassidim is to shower prior to Mikveh, although they are not particular to cut the nails and brush the knots out of the hair during this time. Vetzaruch Iyun.

[7] Michaber Y.D. 198:46; Rambam Mikvaos 1:7; Rosh Mikvaos 28; Rav Beitza 18a “A woman may connivingly immerse with her clothing”; Shach 198:56; Raavan Niddah 327 p. 138a; Sefer Hachinuch Mitzvah 175; Beri Heiytiv of Maharit 198:31; Minchas Yitzchak 4:35; Igros Moshe E.H. 4:14; 4:23-3; O.C. 1:54; Y.D. 4:17; Implication of Rebbe in Igros Kodesh 18:482 in a Limud Zechus of Ben Niddah

[8] See Piskeiy Teshuvos 88:8 that initially one is to remove from the body all items that one normally removes upon bathing. Vetzaruch Iyun on his source as the simple reading of the Poskim ibid do not imply that a differentiation exists between forms of Chatzitzas; See Rama 198:1 in general law; Makor Chaim 198:156