It is asur to do so. If someone is shomer Shabat they are trusted in kashrut.
Of course it isn’t. Firstly, the din of eid echad ne’eman b’issurim doesn’t make it assur to ask. More importantly, trustworthiness only goes as far as that person’s standards, but he is not automatically trusted to keep the standards of his guest, particularly if he is not familiar with them.