The issue here is actually handled by traditional etiquette rules: he who hosts decides the style of the party. If the invitations are going out with the parents as hosts (Mr. and Mrs. S request the pleasure of your company at the marriage of their daughter Nancy S, to Mr. Y ...) then the parents get to decide, because contrary to all the nonsense of it being "the bride's day", etc., the bridal couple are in fact guests at the reception, not the stars of a Vegas lounge act. The CEREMONY is all about their commitment to one another, but the reception is all about sharing joy with people who are close to them -- which kind of doesn't happen when a substantial percentage of the guests are uncomfortable and/or unhappy. Wedding receptions are multigenerational events, so compromise is central to making them enjoyable.
It's simple, really, and pure common sense: you never throw a party in your own honor. Never. And that goes triple on occasions when guests are expected to give gifts. No matter who hosts, the party is supposed to focus on making as many of the guests as happy to be there as possible within the means of the host. If the groom is the one who is most invested in that outcome, then it's great that he is; but regardless of gender, selfishness in a party host is a bad thing. (Which is not to say that one should go bankrupt pleasing the guests; you decide what you can reasonably afford, and then you provide the best experience that you can within that budget.)
So, what happens with the music is that you set it up so that the first part of the party (when the majority of the food is being served) has music that ALL OF THE GUESTS can live with and enjoy to some extent, and then let it change to something that may not suit the tastes of the older contingent, who can be expected to leave early. The bride and groom change out of their wedding clothes before that happens, which is a signal that it is shifting over from wedding reception to young people's party.
Oh, and if you are asking when is it that the bride and groom get to please themselves completely and do whatever they want? The honeymoon, of course!
PS: re the religious aspect of the service? Never push that. The vows are serious business; and it's hypocritical for a person who is does not believe to stand up in a church and pretend otherwise just to please another person. Basing a marriage ceremony on a sham isn't a good basis for getting the marriage off to a healthy start.