“In public someone from Eretz Yisroel visiting chutz la’aretz cannot violate the second day of Yom Tov.”
Nor in private can he violate Yom Tov. He might daven weekday nusach and wrap tefillin in private, but he can’t do melachah even in private.
Certain things are subject to minhag hamakom and others aren’t. A sphard can go to an Ashkenaz shul where the minhag is to wait until marriage for tallis, and he can still wear a tallis in that shul, because everyone knows there’s a diversity of minhagim when it comes to when to wear a tallis.
You have to ask a rav which cases have to defer to minhag hamakom. The assertion that “visiting” makes it not apply is totally incorrect. If I wrap tefillin on chol hamoed and then visit a Sphardic community, I have to do so in private. I can’t walk into shul with tefillin and say, “I’m just visiting!”
I think Joseph might actually be right that with tznius minhagim, you have to immediately defer to minhag hamakom in public, but you’d really have to ask a rav. With the tichel example Shopping gave: Lubavitchers actually hold by davka sheitels in public, but since this seems to be a daas yachid of Chabad, I don’t think anyone would tell a tichel person to switch to a sheitel in Crown Heights. The different minhagim on leggings would be a better question I think.