Ultimately, while I ABSOLUTELY believe in intent mattering when you play a feature character, I do view "intent" as broad rather than narrow. I use Shadowcat as an example, again because she's an oft-abused character:
IF you play Shadowcat you are playing a Jewish girl who likes to dance, is good with computers, and is handy in a fight. She is a Mutant; she phases through walls. She will almost certainly be associated with the X-Men in some manner or possibly Excalibur though she is unlikely to ignore either group even if she winds up further afield, in SHIELD or the Avengers or tending bar in Chicago or something. That is the broad parameter of "intent" I mean when I talk about checking for intent when you app an FC. It's a big landing strip with a lot of places to touch down, but you should still shoot for it rather than parachuting out into the avocado jungle.
You may or may not choose to explore relationships with Colossus, Pete Wisdom, or an acrimonious attraction to ex-husband Star Lord, friendships with Magik, Storm, Cypher, Nightcrawler, Rachel Summers, and a tight relationship with Wolverine. Call those optional parts of the package, or "narrow" intent.
This is not cut and dried with no flex or ability to redefine - I have no theoretical problem with Shadowcat and Magik having a relationship, for instance*. During my roleplay relationships between characters have evolved where when they did appear in canon stories they never got beyond the embryonic stage... so I get wanting to do your own thing. I do.
*In practice hearing about this would send me to the other end of the football field in a hurry unless I knew and trusted both players, because the horror stories about people playing out this as a "romance" run back about... two and a half decades.