Sotah 10b - Feeding people without a Bracha

The gemara says that Avrohom would feed his guests and then explain to them that the food is not his own, but rather from Hashem and that would convince them to make Brachos. Tosafos Shantz quotes the midrash: שלא רצו לברך ברצונם עד שאמר להם אברהם פרעו מה שאכלתם ושתיתם, והיה אומר להם שהוא עולה למנין גדול כי היו במדבר והיה טורח גדול להביא שם המאכל והמשתה, וכשראו כך כי היה רוצה אברהם שיפרעו הכל אז ברכו הקב"ה שלא ברצונם על מנת של איפרעו שום דבר

Basically, through some religious coercion Avrohom managed to get them to make brachos.

The Rama writes in hilchos netilas yadayim (163:2) that one is not allowed to give food to a guest who did not wash netilas yasayim because of lifnei iver. However, the shulchan aruch (169:2) writes that one is not allowed to give food to guests that he knows will not make a bracha [although the shulchan aruch's language implies that you must know they will definitely make a bracha, the biur halacha explains that you can give as long as they are muchzak as kasher and will likely make a bracha). The Rama argues and says that some are lenient if it is being given as tzedaka even if he won't make a bracha. There seems to be a contradiction in the Rama whether one can provide food for poor guests, by netilas yadayim he is machmir [because he doesn't make an exception for tzedaka] and by bracha he is meikil. The Mishna Berura quoting pri megadim seems to understand that if we are sure that he will not make a bracha, as we are sure that he did not wash his hands, you would not be allowed to give him. Based on this, there isn't any distinction between washing hands and making a bracha, rather so long as we are sure that he will not make a bracha, you cannot give him food.

So, how did Avrohom avinu give them food? Although they made a bracha achrona, they ate without a bracha rishona? Of course this question can be answered simply that a bracha rishona was not yet instituted as a chiyuv besides the fact that his guests were not jews, but birchas hamazon is a basic way of recognizing Hashem, so avrohom avinu was makpid about it. A slightly more halachic approach would be that bracha rishona is only d'rabonon so it is lifnei iver on a d'rabonon which perhaps avrohom wasn't machmir about, whereas birchas hamazon is lifnei iver on a d'oraysa.

R' Moshe (Igros Moshe, O.C. 5:13:6) asks what is one supposed to do when they want to feed an apikores. R' Moshe explains elsewhere (O.C. 2:50) that the bracha of an apikores is not regarded as a bracha at all, just as we burn the sefer torah of an apikores without worrying about erasing the names of Hashem since his writing or pronouncing Hashem's name is not sanctified with kedushas Hashem. How then can we give an apikores food, since even if he makes a bracha it will not be regarded as a bracha. R' Moshe explains that if he makes a bracha it is possible that he is doing it based on the instruction of the ba'al habayis and the bracha is being made to Hashem. Although he is a known kofer, we can rely that maybe he is doing teshuva at that moment (like the gemara in kiddushin 49)! Perhaps this gemara complimented by the midrash support R' Moshe's approach, because otherwise it is difficult to understand what avrohom avinu was accomplishing by coercing them to make brachos since they clearly were non-believers. However, in light of R' Moshe's approach we can assume that if we get them to make brachos that they do have the creator of the universe in mind at that moment.