salaam miracle114,
There are my thoughts ...
First, my understanding of "what is dedicated to other than God" (2:173, 5:3) is an offering made or dedicated to an idol (not necessarily physical). For example, some religious traditions practice making "offerings" to idols or deities besides God. If food has not been dedicated to such an idol, it does not come under this category. Further, this applies to all food (whether veg or non-veg), and the religious beliefs or identity of the person serving the food does not matter.
Second, any meat from animals [besides pig] that has been slaughtered by means other than those listed in 5:3 is lawful to eat. And we should mention God's name upon all food that we eat, whether veg or non-veg (6:118-121). And also mention God's name when we hunt or slaughter animals ourselves (5:4, 22:36). And give thanks to God for the food that He has provided (2:172, 16:114). The onus is on the eater to mention God's name upon food that he/she eats. I do not see this as necessitating a religious test on the slaughterer or audit whether he would have also mentioned God's name (or on the fisherman or the farmer for that matter). For example, God says that the food of the people of the scripture is lawful (5:5). There is no requirement to check whether they mentioned the name of God at the time of slaughtering an animal.
Third, the term muslim in the Quran is a descriptive word for anyone who has faith in God and leads a righteous life, without associating partners with Him (2:62, 2:112, 5:69, 3:67). The religious or faith tradition that the person came from does not matter. The classical definition of a Muslim is anyone who testified that "there is no god except God and Muhammad is a messenger of God". The first part of this testimony is indeed the Quranic testimony (3:18), while the second part is described as testimony of hypocrites (63:1) and is not a requirement for salvation. The 'kalima' mentioned in the Quran is consistently la ilaha illallah in various forms, without any creation's name attached to it (37:35, 47:19, 21:25, 2:255, 59:22-23, 21:87 and numerous others). 39:45 describes the disease of the heart of being unsatisfied when God alone is mentioned, and being happy only when others besides God are also mentioned.
My point is that a person who is "Muslim" by the classical definition does not necessarily be one who submits to God by the Quranic definition. Similarly, a person who is "non-Muslim" by the classical definition could well be one who submits to God by the Quranic definition. Ornate, ornamental calligraphy of Muhammad's name, or the graves of Muhammad or saints, or the black stone that people fight to kiss, are not any less of idols than those we normally identify in other religious traditions. There may be people who appear outwardly idolatrous, while having faith in their hearts. God knows the secrets in everybody's hearts, and what they reveal and what they conceal. We should be cautious against being prejudiced against communities that do not carry the label of "Muslim". I do not see a restriction in the Quran to eat only "halal" meat as advertised by people identifying as "Muslims" according to the classical definition.
Peace.