Perhaps you could edit your post to explain what "full native variety" means, and by what means a dialect might be "standardized"? You might also add what research you've done, and what exactly you're hoping for in an answer. Your post is currently too basic and/or broad. :-)

Indian English is spoken by native Indian speakers. American English is spoken by native (North) American speakers. Australian English is spoken by native Australian speakers and so on.

@Mari-LouA "native speaker" is typically used with respect to a language. Here you are using it with respect to geographical areas. It's a bit confusing.

@phoog How is it confusing? Let's pretend my dialect is American English I am a native speaker. I may or may not be living in the US but I speak that dialect. The OP, Eggy, has to make clear what they mean by Native-speakers. Does it refer to any standard English speaker? There must be a standard Indian English but its base will be in that specific dialect. Maybe I'm not understanding, but the OP could definitely clarify and add more detail to their single sentence.

What do you mean by "standardized"? Having had standards imposed upon it?

@Mari-LouA, In Australia, the US and the UK most native English speakers have only very limited exposure to other languages. Is this the case in India? And would you describe an Indian who learned English as a second (or even an additional first) language a native speaker?

@Peter from the little I know, Indian speakers may know more than one Indian language e.g. Hindi and Urdu, while English is taught at schools. A native speaker is someone who speaks the same language as spoken at home or in the region/country they live in. You can be bi-lingual, but if you study a second language you will rarely reach a native-speaker level. It doesn't mean you can reach an advanced level but a native speaker will always know instinctively if a speaker is a learner.

There are many varieties of English in India, varying both by region and by individual education. There is no standard but there are features (pronunciation, vocabulary and syntax) which many of these varieties often have in common and which are less used outside the sub-continent.

There are lots of questions here about individual features of Indian English, and e.g. this one about features that are archaic in the US/UK but current in India. The Wikipedia page also has a lot of information, suggesting it's a group of dialects. Prior to Independence, there was also British Indian English spoken by British people in India.

I think this question hinges on what exactly 'standard language' means. Does it mean 'a consistent collection of phenomena characteristic of a recognizable set of speakers' or does it mean 'a consistent collection... of a prestige dialect' or '... taught in school/has a style guide for media' '...spoken by the most people'?

Can't help noticing discrimination in judging my English, solid, that English, less so.

@Mitch I acknowledge the validity of your question, but I think my question is simpler and I don't want to complicate it too much in how I phrase it. Go back to my example of Australian English. We perceive Australians as speaking Australian English, not "English with a foreign accent." I think many people perceive Indians as speaking English with a foreign accent. That made me wonder whether Indian English is an established variety. If the word "standard" is troubling, perhaps the more general word "established" would help.

I think my question is important because a value judgement is implied when people perceive Indians as speaking English with a foreign accent. If people were aware that Indian English is an established variety, that would lessen the value judgment. Indian English is often mocked and imitated in the popular media, giving it this "foreign" attribute. I myself have often wondered when speaking with an Indian, am I hearing an established Indian English variety, or the foreign accent of a nonnative speaker?

@Yosef Baskin "Standard" and "standardized" are terms in linguistics, and the prestige of varieties is an important topic in sociolinguistics. My purpose in asking my question is not to place a value judgment on Indian English. It's to understand the status of Indian English in linguistics. It's natural for humans to want to classify things to understand them.

I think the difference in perception between Indian English and Australian English may just be due to familiarity. We've had more exposure to Australian through exports like Crocodile Dundee. Also, the Indian accent seems more "exotic".

@Eggy This is an awesome question, and value judgements are undesirable in doing a classification. But a value judgement of prestige (desirability, marker of class) may well be a feature used for to differentiate in a classification. For where I grew up (Virginia), there may well have been a very consistent subvariety of what is called Southern American English (the South of the US, not South America). But I think no one in linguistics would use 'standard' to describe it. I feel like 'standard' has a normalizing, prestige, and codified nature to it. I just don't know if Indian English has that

You have used Australian English as an example of something that is generally perceived as 'a separate standard variety' of English. Perhaps it will help to make the question more focused ig you provide an example of something that you regard as definitely not 'a separate standard variety' of English (so that the question becomes: is Indian English like Australian English or like . . .). Also, are you asking whether Indian English is perceived as 'a separate standard variety' of English (which would, in principle, be answered by polling) or you expect some more objective answer.

@jsw29 Q1: An example from French: The French of Quebec is a standard variety. But the French spoken in northern New England is not a standard variety. It is heavily influenced by English, and most French speakers in this region are native English speakers whose grandparents, not parents, immigrated from Quebec. You rarely meet a proficient French speaker among this population today, other than members of a few organizations that are working to preserve French in New England. Still, when I hear someone speak this type of French, I recognize it as New England French.

@jsw29 Q2: I'm asking whether linguists classify Indian English as a standard variety. I appears that the answer is yes.

Pronunciation (@Eggy) is a less significant factor in defining a variety of English than the choice of words and phrases. People of Indian descent who have grown up in the UK may pronounce words like their neighbours who have no connection to India, but still use stereotypically Indian wording (Reddit thread with some words/phrases)

This is yet another unfortunate case in which a question receives two close-votes soon after it is posted (when its full potential may not be clear), and then the third vote actually closes it, even though the edits, comments, and posted answers have in the meantime developed it into a worthwhile question. In this case, unlike many others that appear on this site, the OP has worked cooperatively with other contributors to give the question 'details of clarity', so it is unfair to dismiss the question as lacking them (just because that may have been the case when it was originally posted).