In standard isolated lab

Question

(Skip this story, that is not part of question, only might be helpful. Sorry for bad English, you can correct things, no stego this time.)
Robot Dan (world smartest vacuum cleaner) and I went to the old isolated lab. It was standard time traveling lab, so kind of cool. However system of time traveling was complicated in calculation date you wanted, because of isotopes it has in it. On machine was big display with simple question: "Centuries?" but on keyboard below were no numbers, just another displays with some pictures, some with puzzles. International organisation for peace made sure to "time travel must be complicated". "Where you wanna go, master?" said robot Dan. I noticed something in my pocket - "What about date on that memorial coin I showed you earlier?" Dan stopped for a moment: "No problem to calculate!" And started to mash symbols. First with guy with laurel on his head (with name Caesar as description), then some Pope. Display changed to: "Years?" and Dan just mashed display with new sofa brand De Lux x, and display changed to: "Months?" Dan mashed symbol with some orchestra and another one with some singers. Not sure what that means, but it even changed years, don't know why. Last symbol for "days?" was with 6 people holding each other with kindness. Dan saw my confused face and said: "Tolerance of course." That puzzled me even more. But suddenly we were somewhere else - or better - sometime else. It was street in London (?) and nothing happened. Only some old guy said (or grumbled?): "Today is stupidest day of this country." I picked up a newspapers from ground (like they do in movies when they time travel) and found what I was looking for.

TLDR:
Find: YYyy-MM-dd (centuries,years-months-days) If you find something overflowing - just add it to higher attribute (eg 25 months = 2 years + 1 month).
YY = Current difference between Caesar and Pope Gregory in days (add 1, since we are currently in future, nothing else changed)
yy = sofa De LuX X
MM = Difference between London Classical Players and Lithuanian Chamber Orchestra.
(might depend on big musical instrument they have, so I don't care if any player is sick or not. Maybe Rudolf or Heinrich could help you with this one.)
dd = Only day in november, when you have to be tolerant to each other. (not that you can't be tolerant any other day…)

And finally it was on 1st day of week. What date it was?

Edit1:

Forgot to mention what year we are in future, which would change YY, but difference would be only "add 1"

Hint 0:

Some random map and 1st day of week means, that is not necessary exactly "dd", but most likely few days earlier.

Answer 1

Full answer:

YY:

14 "According to the new edit"
The difference between a julian calendar and a gregorian calendar currently is 13.

yy:

570
Sofa De LuX X the capitalized letters are roman numerals DLXX = 570

MM: thanks @Gareth McCaughan♦ for your help

1- The text says "heinrich or rudolf" which points to heinrich rudolf hertz
2-" might depend on big musical instrument they have"
Which points to a Piano So combining the 2 together We know that the answer to the clue is the difference between which pitch LCP and LCO tuned their piano to.

The LCP tuned their piano to A=430Hz
And LCO tuned their piano to A= 444Hz
Note that in Europe the frequency of A4 commonly varies between 440 Hz and 444 Hz So the answer for the clue is 14 which is more than 12, so the years will increase by 1 and...

MM is 02

DD:

15
16th of November is the international day of tolerance And it was tuesday that year... But both the title & text indicates the first day of week is monday...

So the answer is:

1971 02 15

Which is the Decimal day And probably the old guy was angry because it's the day that the United Kingdom and the Republic of Ireland decimalised their currencies.

P.s: the meaning of the title..

According to international standard ISO 8601, Monday is the first day of the week.