How would you translate or explain « la fête du slip »? Is it often used in French and in which situation? Is it a very rude expression? (I already know what « fête » and « slip » mean.)
After a quick googling (e.g. https://dico-des-mots.com/definitions/la-fete-du-slip-ou-craquage-de-slip.html) one finds:
[Expression imagée] fête du slip (étymologie) :
(Familier) (Ironique) Décrit un comportement sans-gêne, une situation qui dégénère ou devient absurde, un relâchement total.
[That is, it describes a behavior without embarrassment, a situation that degenerates or becomes absurd, a total relaxation.]
An example of a sentence:
Avec ce gouvernement, c’est vraiment la fête du slip tous les jours !
More information about the origin of the expression is provided below:
[An attempt to translate:]
A popular expression among young people, it derives its meaning from chamber music organizations. The organization and storage must be impeccable and nothing should exceed (especially not underwear!). However, when the end of the service arrived, the military rebelled against the authority by organizing "underpants", decorated the garrisons of underwear and had absurd behavior to challenge the military.
For still more information concerning the so-called event (!) "Fête du slip" described in the last paragraph see the link below:
To supplement Dimitris' excellent answer
Is it often used in French and in which situation?
It is not an expression you will hear all the time, but it is used form time to time. This to say that it is not a dying expression, just one you would use judiciously.
To give you an idea, in a professional setting I heard it a few times over the last years, and used it once or twice.
Is it a very rude expression?
No it is not rude. It is intended to be funny, in a circle you know. Macron would not say it on TV, he may use it during a closed meeting.