The Gemara in Brachot 27a discusses the proper times to pray. Rabbi Yehudah says one can pray mincha until plag; the Rabbis say one can pray mincha until evening. The conclusion is that one can follow either opinion.
The minhag haolam however seems to be to daven minchah and maariv erev shabbos before shkiya, which seems to rely on two mutually exclusive opinions at the same time. Is there a source that this minhag is relying on?
This is a very old practice with many suggested answers. Here are some:
Lechem Mishne (Tefilla 3:2) understands Rambam as holding that since Arvit is a somewhat lower level obligation prayer there's no need to be precise with its timing and we can therefore accept this contradiction.
Tosafot Rosh (Berakhot 2a) understands that while contradictions are generally not a good thing, for matters of prayer we are lenient. His son (Tur 235) expands on that arguing that for a community to have to gather again later is too much effort and hence we are lenient.
Peri Yitzchak (2:9) argues that once one accepts Shabbat the time for Mincha has effectively ended, and hence the time for Arvit perforce starts according to both opinions in the Talmud.
Aruch Hashulchan (235:3) argues that the dispute in the Talmud was about the final time for Mincha but both sides agree Arvit can be recited from 10.75 hours since that's when the limbs of the day's offerings were burned. Accordingly praying Arvit at a time one also would pray Mincha is not a contradiction.
Penei Yehoshua (Berakhot 2a) suggests that there is no earliest time for Arvit and that as soon as one finishes Mincha he can pray Arvit, even shortly after noon. It's the order of the two of them that is important.
Raavyah (83) writes that while avoiding a contradiction is good, if there's a need you don't need to worry about it. He goes on to note (and this was certainly true before the invention of clocks) that such a need is virtually guaranteed at any service that included both Mincha and Arvit back-to-back.
As I understood in the comments, the question is about those daven Mincha, Kabolas Shabbos, and Maariv at the same time throughout the summer without regard to whether Mincha and Maariv are on separate sides of Plag. Many times it comes out that all 3 Tefillos can be between plag and Shkia, so why is there no issue of Tarti Dsasri.
The Mishna Berura in 233:11 brings down a shita that says this is permissible if it will be hard to gather a minyan again.
The Aruch Hashulchan 233:10 explains why this shita holds it is not a problem, he says, since Maariv is representing the Hekter Chalavim and Eivarim which were able to be done by day as well, therefore it is permissible to daven Maariv by day if needed.
מיהו יש נוהגים גם בזה, מפני שקשה לאסוף הציבור עוד פעם (מג"א סק"ז), ויתבאר בסימן רל"ה. ואפשר לומר הטעם כיון דתפלת ערבית נתקן נגד הקטרת איברים, והם כשרים ביום ובלילה, ושם יתבאר בסייעתא דשמיא.
The Shraga Hameir 5:21 strongly defends the minhag on Erev Shabbos to not be makpid on Plag, and offers an explanation that by being Mekabel Shabbos it effectively changes the day and allows for Maariv to be considered being davened on the next day. Obviously this would only work for Erev Shabbos but not on a regular weekday.
