I am decidedly Mutt-American. My wife is Iranian, born in Tehran and later naturalized.
She doesn’t “gate-keep” her culture, but she does insist on being treated with respect, which is perfectly natural and understandable, I think.
For example, she likes when I cook Persian dishes for dinner. I’ve been working on the recipes for a while, and my ghormeh sabzi is better than hers now. (But it’s not better than her mom’s.) Yet even when I take a crack at something and it doesn’t quite come out right, she still values the attempt and the fact that I’m learning.
I have also learned several of the Farsi curses she mutters whenever the kids do something irritating. There’s one that sounds like “akh-staffula,” accompanied by a quick bite on the muscle between the thumb and the index finger, followed by a flicking gesture of dismissal. My wife thinks it’s hilarious when I say it, even though my pronunciation is poor and it’s obvious I don’t know exactly what it means. I’m using it correctly, and that’s what matters.
At the same time, I do enjoy teasing her every now and then. There’s currently a hot button in Iranian culture where their Arab neighbors are trying to change the name of the Persian Gulf, and it’s amusing to “accidentally” refer to it as the “Arabian Gulf” or the “Gulf of Arabia” in passing conversation. My wife is annoyed, but not deeply; she knows it’s just friendly ribbing and I don’t really believe in the name change, and if she honestly asked me to stop, I would. (I talked about it here if you want to know more.)
So, yeah. No gate-keeping at all. Persian culture is fascinating and complex, and my wife likes knowing I want her to share it with me.
(Edit to add, an actual example where I was teasing a little bit and she asked me to knock it off: We were traveling in Istanbul, and she noted how differently the Turks cook their rice, compared to the Persian method. I said, yeah, it’s so much better here! She didn’t laugh. Persians take their rice very seriously. She said, that’s not funny, don’t even joke about that. Okay. Done.)