Do you mean Cage in Lunatic Runagate?
Sadly, we don't get to see many youkais' own personal views regarding the matter. If I recall correctly, even in the games, a lot of the youkai barely acknowledge Reimu as a shrine maiden at all, except when being snarky.
Still, they're firmly aware of the "rules" and the necescity of having a Hakurei Shrine Maiden around, I'm sure (Aya mentions in SSiB that if Reimu doesn't return from the moon, they're going to have to get a new shrine maiden).
Honestly, Reimu could probably beat the vast majority of the lesser ones in a no-holds barred fight, anyways. As for the more powerful ones... well, just read Yuka's section in Perfect Memento for how they tend to treat battles (in a nutshell, they establish rules and formal duels because they know that two high powered beings can fight on with each other possibly endlessly, accomplishing nothing. Considering that Reimu can float beyond reality when she isn't holding back, I imagine a no-holds barred battle of a powerful youkai vs Reimu could potentially go on for a stupidly long pointless amount of time)
Mei Ling claims in EoSD that she should have permission to eat shrine maidens, but this has to be mostly snark, since Reimu snaps at her to not even joke about such things, if I recall correctly. It does imply though that there is a rule AGAINST eating Shrine Maidens for Mei Ling to bring up permission in the first place. From this conversation, it's possible to assume Mei Ling dislikes the rule, but that's not too surprising since she either is new to Gensokyo (if she came in with the Scarlet Mansion) or rebelled against the rules (if she was in Gensokyo before Remilia came along, and then joined Remilia in the vampire incident to go against the other youkai in Gensoky. I lean towards the later)
In Present Day Gensokyo, the (implicitly devil's) contract keeps youkai from eating any resident Gensokyan humans.and that includes Reimu (outsiders might be fair game, though, which does bring to question if Sanae counts. I don't know what you have to do to make yourself get "citizenship" in Gensokyo). The Spell Card rules section of Perfect Memento has the clause where youkai can't kill humans, and Yukari mentions it specifically in one of the latest CiLR chapters, too (although it's possible Yukari's talking about the first devil contract, which forbidded Remilia from eating humans in Gensokyo and probably was extended to all youkai with that clause, since they went to QQ to Reimu aboout it later. Either way, the end result is the same)
Even before the contract, I'm sure there was a long-standing rule from the youkai sages (or at least, an understood unspoken rule) rule that youkai couldn't kill the shrine maidens, since it was pretty clear early on that shrine maidens were needed to maintain the barrier (Perfect Memento in fact implies that youkai were weak from all the restrictions on eating humans, etc, even before Remilia ever came to Gensokyo, and is likely one of the reasons Remilia was able to rampage around so easily). However, without a devil contract, it was more voluntary, so I wouldn't be surprised if a few shrine maidens throughout history met their ends at a youkai that lost control (I also wouldn't be too surprised if that youkai met a mysterious end soon after, either, probabaly hvaing to do with borders and boundaries).
