DY
I dont know about chukas akum. But wihtout question if in a century from now there is a chasidish minhag to celebrate a specidfic day in summer to celebrate fathers, yes It should be obvious that it was copied from goyim.
That said Joseph is silly for the many reasons:
1) “Jews have Father’s Day 354 days a year,” So you agree we should all wish our fathers happy fathwrs day today, you just maintain we should do it tommorow too.
2) Halevai one day a year we have proper kibud av
3) Every day is a time for teshuva, I hope your Rav doesnt discuss teshuva in Elul, every day is time to appreciate Torah, I hope your Rav doesnt discuss these themes on Shavuos. Hodaah on Chanukah, yetzias mitzrayim on PEsach etc etc.
4) These discussions are absolutly silly becasue the bottom line is this: If a father apreciates father’s day then there is no question that there is a mitzva deoraisa to wish him happy father’s day, if he doesnt care there is no reason too. Thus your opinion is only relevant to your children. So spare us.