From the way the Seth/Eirika supports go, one might assume that marriages between royalty and their knights are forbidden in Magvel.  The way the entire Ismaire/Carlyle fiasco plays out lends this some support, and a good deal of fanfic and meta uses this assumption as a springboard in any event.

On examination, though, is it really the case?  Consider the counter-evidence.

1) Seth/Eirika paired ending.  "[They] were wed, with the blessings of Ephraim and all the Knights of Renais.  The tale... became a beloved romance in Renais."  Sounds like nobody objects, then.

2) Joshua and his ladies.  Both the ending with Natasha (his "perfect companion") and the one with Marisa indicate no hint of turmoil, and you might imagine that the citizens of Jehanna would be a wee bit leery of unconventional relationships.  Apparently not.

3) Innes/Vanessa.  All of it.  Not to mention their paired ending also states they "lived happily with the blessing of all around them."  And while Joshua might be pegged as a renegade royal who does things his own way, I don't recall any indication that Innes is a particularly oddball Prince of Frelia.  If anything, he's presented as the opposite, a royal heir who strives to fulfill the common expectation of what the role requires.  He's got no problem at all hooking up with one of his knights (even if we assume he doesn't marry her) and apparently no one else is bothered by it, either. 

In fact, the royal marriage that does cause public outcry is the union of Ephraim and L'Arachel, which "throws Rausten into turmoil" for whatever reason.  Interesting.  

World-building in Magvel being what it is, we know next to nothing about the marriages of any of the senior representatives of the royal houses. We don't know if Fado, Vigarde, and Hayden married nobles/clerics from their own courts, or foreigners, or perhaps members of their own retinue of knights[*].  As the game doesn't mention any of the royal heirs being closely related, it's not too likely that Fado married Hayden's sister (for example), but that's still within the realm of possibility.

But, aside from the situation of Carlyle and Ismaire-- a unique situation of a ruling queen with a dead husband and a missing son-- there's not really hard evidence that matches between royalty and commoners are forbidden.  In Ismaire's case, a second marriage could potentially result in a "king" of Jehanna whose progeny could break the line of descent from Jehanna's unnamed founder, so Carlyle's situation is especially problematic.  He's got more against him than just being a commoner, even if we assume (again) that second marriages are even allowed in Magvel.  As crimsonmorgans pointed out, they might not be.  We don't have positive evidence for second marriages being acceptable.
 
At any rate, while the marriage of Eliwood to either Fiora or Lyn in FE7 is stated to cause conflicts/uproar, we don't see anyone in Magvel throwing fits over Joshua bringing home a cleric from Grado, or even over Eirika going off to nowhere land to live with some dude in the mountains.  The only thing the public won't take, apparently, is L'Arachel Princess of Light taking the Restoration King as her husband.  (Again, interesting.)

So, what's up with all the objections raised in the Eirika/Seth supports?  Well, it could be a couple of things.  There could be a double standard for acceptable behavior in princes and acceptable behavior in princesses.  There might be a different standard of conduct in Renais, the nation with no female knights or generals, compared to Frelia.  Or the whole dynamic could say more about Seth and Eirika, their personalities and self-perceptions and fears, than about Renais in particular or Magvel in general.  Note the vast difference in tone between Eirika's supports with Seth and her supports with Forde.

I tend to think Seth's objections are coming from more of a personal level.  The way Eirika made him feel during their escape rattled his self-perception and some of his own core assumptions re: duty and social roles, and I don't think that can be underestimated.  He wasn't expecting that.  From the way he speaks of it in their A-support, it got to him deeply.  And if the great knight of Renais can feel that way for his princess, what else might be he capable of that he doesn't even know or expect?  Over the course of the war, Seth sees more than enough of the damage caused by obsessive love; he wouldn't want to even think about risking Eirika and everything else he values.  The cost, as seen in the antics of Orson, Carlyle, and Lyon, would simply be too great.  And Eirika, at least in the course of their conversation, does echo the objections as Seth defines them.

And then she marries him anyway.  Hmm...

* A fair possibility for Hayden, in any event, especially as royal women serve as Pegasus Knights.