In Bamidbar 17:1 we see that Korach decided to fight regarding the Kehuna. The Gemara in Horiyus 28b says that from the word “vekidashto” we learn that one has to give precedence to a Kohen regarding any davar shebikdusha. The Kohen bentches and gets the first portion etc.
In Gittin 59b we see that the chiyuv of kedushas Kohen is Min HaTorah. The Rambam in Sefer Hamitzvos 32 and the Smag 171 say that the chiyuv of vekidashto is a de’Oraysa. Tosfos in Chullin 87a says that if a Yisroel took the first aliyah he does not have to pay the Kohen 10 gold pieces which is usually paid to someone who had a mitzvah done by someone else without permission. The reason for this is that the posuk of vekidashto is just an asmachta. The Rosh 8 agrees with Tosfos.
In Shailos Utshuvos Rivash 94 there was a question posed whether a person should be more severely punished if he curses a Kohen. The Rivash says that despite the fact that vekidashto is a de’Oraysa, nevertheless, if the Kohen who was cursed is an Am Haaretz and does not keep the mitzvos as befitting a Kohen, the punishment does not have to be any more severe. He brings the Gemaras in Menachos 53a and Yoma 71a that says that the Chachamim did not hold back from cursing the Kohanim families they felt were not behaving properly or if they did not have full yichus. We therefore could reason that of course in our day and age where the Kohanim don’t have yichus, but rather just a chazaka that they are Kohanim, of course, one should not get punished in a more severe way for cursing them.
The Yefei Mareh in Yerushami Brachos 8:2, where it is discussed if a Yisroel is mishtamesh with a Kohen, it states that he is moel be’hekdesh. The question is why in today’s day and age are we not careful in this halacha? He answers that we could be melamed zchus since today most Kohanim are not meyuchasim. The Mishna LeMelech in Hilchos Avadim 3:8 argues with the Yefei Mareh and says in the case of the Rivash, where one wants to punish a person who cursed a Kohen, we can’t be machmir and punish him in a worse way as we have no proof that the Kohen is a meyuchas. However, one cannot use a Kohen to do something for him and it is considered me’ilah be’hekdesh since he is a safek Kohen. From the Rivash we can learn that if one is a Kohen who is an Am Haaretz, one may use him and not worry about meilah be’hekdesh.
In Hilchos Birchas Hamazon 201:2 the Mechaber says one should not let a Chacham Yisroel bentch in the place where there is a Kohen who is an Am Ha’aretz present, but the Kohen may give reshus. In the case where the Kohen is a Talmid Chacham, one must give the bentching to him as there is the mitzvah of vekidashto. The Mechaber does not differentiate in different eras, but rather in all time periods, the Kohanim have the same halacha. The Magen Avraham 4 asks why are we not makpid on this today? He answers that we are not baki in yichus of Kohanim. The Mishna Berura 13 says that if there is a Kohen who is a Talmid Chacham present, you must afford him preferential treatment. The Chazon Ish in Shviis 5:12 asks that despite the fact that the Kohanim are not meyuchas, we still find that they make berachos on duchening and pidyon haBen, so why should they not be afforded preference? The Rev Pe’alim in Orach Chaim 2:39 argues and says that our Kohanim are not meyuchas, but they get the first aliyah beToras minhag. That is why they duchen; so the mitzvah of nesias kapayim should not be nisbatel, and they therefore make a bracha because of the minhag. The bottom line is that as far as a Yisroel is concerned, he needs to rely on chazaka and get nesias kapayim and Pidyon HaBen, so he therefore should show respect because of the minhag. As far as a Kohen demanding it, he might not be in the right, since today we don’t really have Kohanim meyuchasim.
May we all be zocheh to be the am hameyuchas and see Moshiach, Amen!