The primary prohibition is limited to meat that is slaughtered by them because it will not be slaughtered in Allah's name, and it may be dedicated to their gods rather than to Allah.
Quran 6:118 So eat of that [meat] upon which the name of Allah
has been mentioned, if you are believers in His verses.
Quran 6:121 And do not eat of that upon which the name of
Allah has not been mentioned, for indeed, it is grave disobedience.
And indeed do the devils inspire their allies [among men] to dispute
with you. And if you were to obey them, indeed, you would be
associators [of others with Him].
Quran 6:145 Say, "I do not find within that which was revealed to
me [anything] forbidden to one who would eat it unless it be a dead
animal or blood spilled out or the flesh of swine - for indeed, it is
impure - or it be [that slaughtered in] disobedience, dedicated to
other than Allah . But whoever is forced [by necessity], neither
desiring [it] nor transgressing [its limit], then indeed, your Lord is
Forgiving and Merciful."
Quran 2:173 He has only forbidden to you dead animals, blood, the
flesh of swine, and that which has been dedicated to other than Allah
. But whoever is forced [by necessity], neither desiring [it] nor
transgressing [its limit], there is no sin upon him. Indeed, Allah is
Forgiving and Merciful.
Apart from this several other prohibitions also come into effect. Halal food can not include pork, carrion, blood, wine or an animals slaughtered by other than the exsanguination (see 5:3 and 5:90). Hindu food will normally not meet this requirement, and even when it is not meat itself, it may have ingredients of animal origin which may not be halal.
As such, meat is only permitted in Islam when it has been slaughtered by a Muslim, a Jew or a Christian:
Quran 5:5 This day [all] good foods have been made lawful, and
the food of those who were given the Scripture is lawful for you and
your food is lawful for them.
Their purely vegetarian food is permitted, however a secondary prohibiton may arise when it is contaminated by food that is not permitted to Muslims. This also makes eating in their utencils forbidden when the same utencils are used to serve haram food ... however the material najasat (impurity) is inherent to the food and not to the people themselves.
From Tafsir Al Qurtubi on 5:5
ولا بأس بأكل طعام من لا كتاب له كالمشركين وعَبَدة الأوثان ما لم يكن من
ذبائحهم ولم يحتج إلى ذكاة؛ إلا الجُبن؛ لما فيه من إنْفَحة الميتة
For such people there is nothing wrong with eating their food when
they are not People of the Book, such as polytheists and idolaters,
when it is not of their slaughtered meat ... except cheese because it
may use [rennet] from a dead [or haram] animal.
ولا بأس بالأكل والشُّرب والطَّبخ في آنية الكفار كلهم، ما لم تكن ذهباً
أو فِضّة أو جِلد خِنزير بعد أن تُغسل وتُغلى؛ لأنهم لا يتوقّون النجاسات
ويأكلون الميتات؛ فإذا طَبَخوا في تلك القُدور تنجّست، وربما سَرَت
النجاسات في أجزاء قُدور الفَخَّار؛ فإذا طُبخ فيها بعد ذلك تُوقّع
مخالطة تلك الأجزاء النّجسة للمطبوخ في القِدر ثانية؛ فاقتضى الوَرَع
It is permissible to use the utencils of the disbelievers to eat,
drink and cook ... when they are not made of gold, silver or the skin
of pigs etc. But the utencils should be washed before use, because
they do not refrain from impure foods and eat swine and carrion, and
when they use the utencils to cook they are made impure, and sometimes
the impuritites get stuck in the pores of pottery and may contaminate
whatever is cooked in it.