Positive word for someone who wants to get into relationships with rich people
I think opportunist would be the word for someone who wants to get into relationships with rich people so that they can get rich, but that word is negative and can be used for other situations as well. Do we have a more accurate word for it?
A social climber may suggest the idea and doesn't necessarily have negative connotations:
a person who attempts to gain a higher social standing.
a person who tries to gain acceptance to a social stratum above the one he or she currently occupies.
The Free Dictionary
Ambitious is suitable:
adjective
1 Having or showing a strong desire and determination to succeed:
If your measure of success is wealth, then hooking up with a rich person seems like a reasonable strategy. Like the OP and other answers provided, it can elicit either positive or negative connotations, and it can easily be applied to various situations. The history of ambitious connects it firmly to the notion of relationships:
(adj.) late 14c., from Latin ambitiosus "going around to canvass for office," from ambitio (see ambition).
mid-14c., from Middle French ambition or
directly from ambitionem (nominative ambitio) "a going around," especially to solicit votes,
hence "a striving for favor, courting, flattery; a desire for honor, thirst for popularity,"
noun of action from past participle stem of ambire "to go around" (see ambient).
As you say "gold digger" is wholly negative, and is often used, by for example, people who foolishly married badly with no regard to education, economic status etc.
I don't have a more accurate term (as you ask) which is neutral.
However, there are two terms which are commonly used in this situation. These are "practical" and "sensible".
She was very practical about marriage.
Note: as Scott has pointed out, add "ambitious" to this list.
These three words CAN BE used in a straight, neutral way. "My daughter made a sensible marriage." "Fortunately Annie made a practical marriage instead of getting pregnant at 17 to that boy with the motorbike."
However, note that indeed the three terms can be used "with a wink" as euphemisms, to imply the same sort of gold-digger-language disapproval.
(I mean all of this in typical AmE or BrE ... of course in many countries arranged marriage, etc., is the norm and it would seem bizarre to marry for purely emotional reasons.)