Lacking the intellectual infrastructure to think through policies on its own, BJP often just toes the Congress line, even when this explicitly goes against the party’s own stand in opposition and outrages its supporters.
Also, what is 'stand in opposition'.
I think the sentence is grammatically perfect but Grammarly shows up a problem with the possessive used with the party.
To answer your first question, about "intellectual infrastructure":
Look at the definition of infrastructure in this dictionary. In this case, we use the first meaning - the general underlying framework, physical or not, to support any system. In this case, that system is a political party (the BJP).
So "intellectual infrastructure", in the context of a political party, would mean things such as think tanks, advocacy groups, political journals, political philosophers, newspaper editorial boards, etc. - the intellectual support for the political party. The author is saying that the BJP doesn't have these.
An infrastructure is comparable to a skeleton - it provides the base that something can be built on, but also allows things built on it to move around and develop/grow/flourish. A bad infrastructure will limit the extent or speed at which something can develop or change.
Lacking the intellectual infrastructure to think through policies on its own, BJP often just toes the Congress line, even when this explicitly goes against the party’s own stand in opposition and outrages its supporters.
Stand is a noun meaning "official point of view".
X in opposition means "against and attempting to fight/overcome a existing established X"
Your tool may be thinking stand is a verb, which it is not. The possessive determiner own is OK with stand as a noun.
