It is a good question and the answer to the specific example here is no, it would not be permissible. The concept of not following their ways is not only restricted to religious elements. It applies to their distinctive habits and customs (minhagim) anything that in a specific time period distinguishes between traditional Jewish behavior and fashionable, non-Jewish behavior.
For example, what follows is from Kitzur Shulchan Aruch 3:2 dealing with clothing and modesty.
We do not act in the ways of the nations, and we do not emulate them--not in dress, nor in hair style, and the like--as it says, "And ye shall not walk in the customs of the nation" (Leviticus 20:23). And as it says, "Neither shall ye walk in their statutes" (Leviticus 18:3). And as it says, "Take heed to thyself that thou be not ensnared to follow them" (Deuteronomy 12:30). One must not dress in clothing unique to them for pride, i.e. clothing worn by officers. For example, it is stated in the Gemara (Sanhedrin 74a) that it is forbidden for a Jew to act like them, even regarding shoelaces. If they would tie [their shoes] in one way, and Jews would tie another way, or if their custom was to have red laces, and Jews would have black (for the color black is instructive in humility, lowliness, and modesty), it is forbidden for a Jew to differ. And from this every person should learn, according to his time and place, that the clothing that is made for arrogance and licentiousness--a Jew may not use it. Rather, his dress must be made in a way that is instructive of submissiveness and modesty. So it is said in the Sifri that you must not say, "Since they go out in purple, I too will go out in purple," or "Since they go out with kolasin, i.e. weapons, I too will go out with weapons." For these are matters of arrogance, and this is not the portion of Jacob. Rather, their [the children of Jacob] way is to be modest and humble, and not to turn toward conceit. And so too anything which they [the nations] do that can be suspected of containing an iota of foreign worship, a Jew may not do it. And so he may not shave his head or grown his hair like them. Rather, he must separate himself from them in dress and speech and in all his other actions, just as he separates himself from them in his knowledge and opinions. And so it is said, "And I have set you apart from the peoples" (Leviticus 20:26).
This is also the view expressed in Shulchan Aruch, Yoreh Deah 178:1 which states:
אסור ללכת בחוקות העובדי כוכבים וא"צ לומר שלא לקסום ולנחש ולעונן שכל אלו מפורשין בתורה דכתיב לא תלמד לעשות כתועבות הגוים ההם לא ימצא בך מעביר בנו ובתו באש קוסם קסמים מעונן ומנחש ומכשף וחובר חבר ושואל אוב וידעוני ודורש אל המתים אלא אפי' מנהג שנהגו אסור לילך בו דכתיב ובחקותיהם לא תלכו וכן כתב הרמב"ם אין הולכין בחוקות העובדי כוכבים ולא מדמין להם לא במלבוש ולא בשער וכיוצא בהן אלא יהיה הישראל מובדל מהם וידוע במלבושו ובשאר מעשיו כמו שהוא מובדל במדעו ובדעותיו ולא ילבש מלבוש המיוחד להם ולא יגדל ציצית ראשו כמו ציצית ראשם ולא יגלח מן הצדדין ויניח השער באמצע כמו שהם עושין וזהו שנקרא בלורית ולא יגלח השער מכנגד פניו מאוזן לאוזן ויניח הפרע ולא יבנה מקומות כבנין היכלות של עובדי כוכבים כדי שיכנסו בהם רבים כמו שהם עושין וכל העושה אחד מאלו וכיוצא בו לוקה. מי שקרוב למלכות וצריך ללבוש כמלבושיהם ולדמות להם מותר בכל:
The conclusion of this halacha is the basis for the possible prohibitions related to sports stadiums. It reads that we do not build big palaces like they do, for big communal meetings. The commentaries to this section of Shulchan Aruch explain that this was related to the Colliseum, not their places of worship. The Colliseum was the site of the gladiator contests and other public sporting events. What transpired at those sporting events was very much the opposite of traditional Jewish behavior. And as is mentioned in a related question already on this site, that was the view expressed by Rav Moshe Feinstein.
