Prohibition of kilayim and Bnei Noach
The Gemara (Sanhedrin 56b) quotes a dispute about this question. According to the Sages, the prohibition of kilayim does not apply to Bnei Noach, whereas according to Rabbi Elazar, Bnei Noach are included in some of the kilayim prohibitions but not others. Specifically, they are prohibited from mating different animal species and from grafting one species of fruit tree onto another, but they may plant different species together or in a vineyard, or wear shatnez.
Why are they included in one prohibition but not the other?
Describing the creation of plants, the Torah says: “And G-d said, ‘The earth shall sprout forth vegetation, herbage that produces seed; Edible trees that produce fruit of their own species’. And the earth produced vegetation, herbage that produces seed of its own species and trees that bear seed-bearing fruit of their own species.” (Breishis 1:11-12).
Reading the pasuk carefully, we see that Hashem ordered only the trees, and not the herbaceous plants, to “produce fruit of their own species.” Even though the herbage did in the end produce “seed of its own species,” this was not because it was commanded. The Gemara derives from other sources that just as the earth was commanded to keep tree species distinct, so too, Adom HaRishon and all his descendants were commanded to keep these species distinct. But since the herbaceous world was never commanded to keep its species distinct, Adom was not commanded concerning this halacha. Therefore, although Jews may not plant them together, Bnei Noach may (Yerushalmi Kilayim 1:7, quoted by Gra to Yoreh Deah 295:2).
The Rambam (Hilchos Melachim 10:6) rules like Rabbi Elazar that a non-Jew may not graft one species of tree onto another, whereas the Ritva (Kiddushin 39a s.v. Amar Rabbi Yochanan) and the Shach (Yoreh Deah297:3) are lenient. Although we usually follow the Rambam’s opinion, some poskim suggest that we might be able to rule leniently if only a rabbinic prohibition is involved, such as where the grafted tree exists already and one is not watering or pruning it (Chazon Ish, Kilayim 1:1).