Is there such a thing as a kosher replacement for the egg on the Pesach plate?
I just don't like an invited guest making a comparison to the Easter egg.
The Gemara (Pesachim 114b) tells us what different amora'im held one should eat in fulfillment of the two cooked dishes, and so obviously there are kosher alternatives (though maybe not the option of rice if you have a custom not to eat it).
But even if there are alternatives, wouldn't it be better to consider learning the significance of the egg instead of avoiding it because of resemblance to the Easter egg?
The Gemara tells us that the two cooked dishes are in commemoration of the pesach sacrifice and the chagiga sacrifice. The Tur (473) says that the custom is to use meat and an egg for the two cooked dishes. The meat is an arm bone in commemoration of the "outstretched arm" of the Exodus, and the egg (ביעא) is used for phonetic resemblance to the word "seek" (בעי), making together בעי רחמנא למפרק יתנא בדרעא מרממא "God seeks to redeem us with an outstretched arm" (Beit Yosef quoting Kol Bo quoting Yerushalmi).
So there is symbolism to the choice of an egg, even if it isn't a requirement, and there's no reason to feel uncomfortable with it because of a resemblance to a Christian custom.
Mishnah Pesahim 10:3 states:
הביאו לפניו מצה וחזרת וחרוסת ושני תבשלין
They bring before him matzah, lettuce, haroset and two cooked dishes.
As we will see, these 'two cooked dishes' are what we now know as the zero'a (shank bone) and beitzah (egg) that are commonly found on the seder plate.
Talmud Bavli Pesahim 114b clarifies:
מאי שני תבשילין אמר רב הונא סילקא וארוזא רבא הוה מיהדר אסילקא וארוזא הואיל ונפיק מפומיה דרב הונא ... חזקיה אמר אפי' דג וביצה שעליו רב יוסף אמר צריך שני מיני בשר אחד זכר לפסח וא' זכר לחגיגה רבינא אמר אפילו גרמא ובישולא
What are the two cooked dishes?
Rav Huna said, "Beets and rice". Rava was particular to use beets and rice, since these had been mentioned by Rav Huna...
Hezekiah said, "Even fish with a coating of egg upon it (counts as two cooked dishes)".
Rav Yosef said, "One needs two kinds of meat, one as a remembrance of the korban pesah and one as a remembrance of the korban hagigah."
Ravina said, "Even a bone with its gravy (counts as two cooked dishes)".
So we see from the gemara itself a wide range of options for what to use.
Rambam Hilhot Hametz uMatzah 8:1 actually writes (seemingly in accordance with the view of Rav Yosef):
ובזמן הזה מביאין על השלחן שני מיני בשר אחד זכר לפסח ואחד זכר לחגיגה
Nowadays [in the absence of the temple] we bring to the table two kinds of meat, one as a remembrance of the korban pesah and one as a remembrance of the korban hagigah.
However, Shulhan Arukh Orah Hayyim 473:4 writes:
ושני תבשילין אחד זכר לפסח ואחד זכר לחגיגה ונהגו בבשר ובביצה
And two cooked dishes, one as a remembrance of the korban pesah and one as a remembrance of the korban hagigah, and they are accustomed to use meat and an egg.
Bottom line, one can definitely fulfill the Talmudic requirement with any other cooked dish in place of the egg.
However, whether it is appropriate to deviate from a long-standing custom in deference to unwanted comments from guests, is a question best asked to a competent, local rabbi.