Yes, the rules of grammar and punctuation keep on changing in the world today. The rules being followed are dynamic in nature and change according to the trends followed in the society.
A number of the changing trends have found their way into the English language which has caused extinction of a few grammar rules. However, it is necessary that we should know the pre-existing rules in order to cope-up with the changes.
Some of the relative rules that have changed in the 21st centaury are:
splitting of infinitives
The use of period/full stop
Do not start a sentence with a conjunction
The use of each other and one another
Therefore, there have been changes in the rules of grammar and punctuation.