The Jewish Worker points out two contrasting midrashim. In Bava Metzia daf 86b:
Let a little water, I pray you, be fetched, and wash your feet: R. Jannai son of R. Ishmael said: They [the travellers] protested to him [Abraham], 'Dost thou suspect us of being Arabs, who worship the dust on their feet? Ishmael has already issued from thee.'
This is not necessarily punishment that his descendants will act this way (after all, hakol biydei shamayim chutz mir`at shamayim), but rather that Yishmael has already been born and is presently acting this way. So don't point fingers at others, who happen to be innocent, when you already have this going on in your own house.
In contrast, Rashi makes this suspicion into a positive thing:
|and bathe your feet: He thought that they were Arabs, who prostrate themselves to the dust of their feet, and he was strict not to allow any idolatry into his house. But Lot, who was not strict, mentioned lodging before washing, as it is said (below 19:2): “and lodge and bathe your feet.” - [from Gen. Rabbah 54:4]||ורחצו רגליכם: כסבור שהם ערביים שמשתחוים לאבק רגליהם והקפיד שלא להכניס עבודה זרה לביתו. אבל לוט שלא הקפיד, הקדים לינה לרחיצה, שנאמר (יט ב) ולינו ורחצו רגליכם:|
Does Rashi change the midrash, or its tone? On occasion, Rashi does indeed do this. And in those instances, we get a sense of how Rashi harnesses midrashim and directs them in a way to present peshat. But this is not one of those instances. Jewish Worker was misled by the Mikraos Gedolos, which puts the source for Rashi as that gemara in Bava Metzia. Rather, as Judaica Press' chumash with translation notes, he gets this from Bereishit Rabba:
אל בית עבדכם ולינו ורחצואברהם מקדים רחיצה ללינה, ולוט מקדים לינה לרחיצה?!שאלא, אברהם מקפיד על טינופת עבודת כוכבים, לפיכך הקדים רחיצה, ולוט אינו מקפיד על טינופת עבודת כוכבים.ויש אומרים:אף זה עשה כשורה, כדי שיצאו ויראו אבק על רגליהם, שלא יאמרו היכן לנו.
Rashi's concern appears to be, here, how Avraham is a great guy. And also perhaps the contrasting of the two greeting stories. Rashi certainly bases himself on Bereishit Rabba, and he selectively cites the midrash. He does not cite the yesh omrim here, that Lot acted appropriately.
However, interestingly enough, Rashi contradicts himself. While he cites the avodah zarah concern local to the Avraham and the malachim story, local to the Lot and the malachim story he puts forth as the only peshat that Lot acted appropriately, because of particular circumstances; while Avraham acted in the entirely customary manner:
|and stay overnight and wash your feet: Now is it customary for people to first stay overnight and afterwards to wash? Moreover, Abraham said to them first, “and wash your feet!” But so did Lot say (i.e., he reasoned), “If, when the people of Sodom come, they will see that they have already washed their feet, they will invent false accusations against me and say, ‘Two or three days have already passed since they came to your house, and you did not let us know!’” Therefore, he said, “It is better that they remain here with the dust on their feet, so that they should appear as though they had just arrived now.” Therefore he said, “Stay overnight” first and afterwards, “wash.” - [from Gen. Rabbah 50:4]||ולינו ורחצו רגליכם: וכי דרכן של בני אדם ללון תחלה ואחר כך לרחוץ, ועוד שהרי אברהם אמר להם תחלה (יח ד) ורחצו רגליכם. אלא כך אמר לוט אם כשיבאו אנשי סדום ויראו שכבר רחצו רגליהם, יעלילו עלי ויאמרו כבר עברו שני ימים או שלשה שבאו לביתך ולא הודעתנו, לפיכך אמר מוטב שיתעכבו כאן באבק רגליהם שיהיו נראין כמו שבאו עכשיו, לפיכך אמר לינו תחלה ואחר כך רחצו:|
There might be all sorts of ways of resolving these apparently (and I believe indeed) contradictory midrashim, both of which Rashi appears to put forth as peshat. Siftei Chachamim does not address this issue. My own guess is that Rashi is trying to develop two different themes in these two places, and cites the midrash that helps advance the particular theme, without really paying heed to whether two midrashim end up contradicting one another.
Update: See the comment section, with Soccer Dad's comment and my reply. As Artscroll on Rashi and Mosad HaRav Kook's Rashi both note, this second Rashi was not in the first printing of Rashi. See here in Yosef Daas where he brings this text from a klaf as well as another sefer of Rashi. If so, we can eliminate the contradiction. The harmonization offered in Artscroll, though, I don't like, for reasons I detail below in the comment section.