We make backlinks for our website as SEO methods, but we find all profile backlinks and some web 2.0 blog sites page never indexed by Google, is those backlinks we made on those page can get any benefits for SEO?
If they are not indexed on Google, it means that search engine does not count them at all. You need to remember that Google is not the only search engine out there, though. Many people use others to avoid Google tracking. DuckDuckGo is increasingly known as a reliable Google competitor.
Profile links do not get indexed anymore. If you build tens of thousands of profile links using xrumer or GSA SER, you will find only few of them being indexed month or two later. None of the indexer services work anymore either so luck on getting those profiles indexed using those indexer services. Web 2.0 pages will not get indexed by itself. Only way to get them indexed is by building links to them.
If you build links on pages that are set to no-index from the meta or in any other way, set as non-index - then it won't help you seo efforts. That being said, if a page is simply not indexed as of today but has the potential of getting it indexed in the future then building links on them isn't a complete waste of time. Profile links, or other web2.0 easy to get links might not be indexed today, but they can get indexed later someday - so it might not be a total waste of time.
It is still good to have a mix of all types of links and traffic sources. Your website will get flagged if your backlink profile does not look natural. For example, having 90% do-follow links as opposed to an even mix of no-index/no-follow/follow Also, no-follow is just a guide for Google. They will count the link in if they think it is relevant.
If a given link is not indexed, it means that its value is small. Remember that some backlinks may be indexed for up to six months.
If they aren't indexed on Google it means they don't have any real value so you will not see any impact on SEO from them. Try to figure out why they aren't indexed and see how you could fix it in the future, as it's important that you submit articles and pages properly so that algorithms can scan the content on it and give you ranking.
If the links aren't indexed on google, how could they possibly confer any sort of benefit? Afterall, Google doesn't know about them.