The fact is that new users ARE a burden on the community initially. They aren't familiar with how the community operates yet, they are disruptive and they often need help to learn how to fit in the community well. They have a lot they can bring to the community, but it takes an investment to get those dividends.
Since it does take effort to help them fit in, reward those who help new users regularly. The main reason communities tend to become resistant to new users is that they feel like the new users detract from the community. If you can focus at least some rewards around helping these new users, it makes the new users a means to an end instead of an annoyance from normal enjoyment of the site.
This can specifically look like a lot of different things depending on the community, but the key is to make it so that new users are of more benefit to experienced users than they are a burden. It may be badges, reputation, public acknowledgement, granting extra privileges or something else entirely.
Leading by example also helps a lot in being welcoming and supportive of new users, as does ensuring that there are sufficient quality resources available to help new users come up to speed as quickly as possible so that they are less of a burden on the community to begin with.
It also may not hurt to feature particularly good posts by newer users that demonstrate the value that new users do bring in the long run. This may help with reinforcing that new users are worth the effort even if they bring some pain up front.