Chassidim commonly keep the times according to the decisions of Rabbeinu Tam who considers sunset to be later than the generally accepted time. Many people keep the times of Rabbeinu Tam only "l'chumroh", meaning they accept Shabbos at the normal time and do not do melacha after the normal time, but keep Shabbos on Saturday night until the later time of Rabbeinu Tam.

Some people however, a number of hassidic groups in particular, keep the Rabbeinu Tam times completely, not just l'chumroh. They start Shabbos according to the later times, they will not daven maariv before the later times, etc.

When I was first learning in depth the issues of the times and learned that some people keep the later times completely and not just l'chumroh, I asked some hassidic friends (from different groups) what they do. I got mixed results, but some definitely told me they follow the times of Rabbeinu Tam completely and not just l'chumroh.

Kikar is reporting on a psak of Rav Elyashiv that disputes the rights of any specific hassidic leader and group to follow Rabbeinu Tam times completely, and only allows it l'chumroh. An unnamed hassidic rebbe determined that a baby born on Monday evening, 20 minutes after sunset, should be circumcised the following Monday (rather than Tuesday), as 20 minutes after sunset is still considered Monday, as it is before the sunset of Rabbeinu Tam. The psak was nothing new, as this hassidic group, among others, follow the Rabbeinu Tam times completely.

The situation was presented before Rav Elyashiv who was shocked to hear that the baby would be circumcised on Monday instead of Tuesday. Rav Elyashiv said that by doing so they are transgressing a, issur d'oraisa, and it doesn't matter how many thousands of hassidim are affected and must redo their bris milah (by being required to perform a hatafas dam bris), and it does not matter how old they are.

When asked that they are hassidim and keep that psak of Rabbeinu Tam, Rav Elyashiv supposedly responded that what does it matter that he is a hassid? Do Hassidim not keep the Torah? The accepted psak has been NOT like Rabbeinu Tam.

According to Rav Elyashiv's psak, if reported accurately, any person circumcised according to the times of Rabbeinu Tam will have to consider himself having been circumcised on the 7th day rather than the 8th day, and will be required to do a hatafas dam bris to rectify it.

I don't know what happened to "eilu v'eilu" and why hassidim are not allowed to keep the times according to the psak of their leaders, but so Rav Elyashiv is being quoted..