Hi, and welcome to the forums.

Recognize that the singular their is well established as an alternative to 'his/her.' If you want to make them parallel, make individuals singular, so it doesn't look like people have multiple partners. Whether their as a singular pronouns is appropriate for an academic paper is another matter.

avoidance occurs when individuals strategically refrain from broaching an issue with their partner.
: individuals is plural, their is singular (assume), is this acceptable?  I find this accepable. But I prefer "an individual... their partner" to be clear about the 1:1 relationship.

The subject of the sentence is plural, and yet the part of the sentence is not directing referring to that (plural version), but rather a singular version by the use of their as singular.
: if plural their is used, then it would mean the entire group of individuals only has one partner, would is a bit of nonsense And the fact that the reader knows that not every individual shares the same partner helps make this sentence work.

avoidance occurs when an individual strategically refrains from broaching an issue with their partners.
: this would almost undoubtably mean an individual has multiple partners, rather than 'their' being used as plural, to indicate one partner for each individual.

I hate to disagree with MH, but when I see "an indivdiual" and "partners" I assume it means each individual has more than one partner. If it meant only one, then it would say "partner." If the writer wanted to show the possibility for one or more than one, then he or she can use "partner(s)."

avoidance occurs when individuals strategically refrain from broaching an issue with their partners.
: the intended their is plural, but since it can also be singular, it may look like an individual has multiple partners (given that 'the above' is verified to be acceptable)
: if the intended meaning of plural their is used, then it would mean one partner for each individual, or one-to-one relationship This version is ambiguous. I could mean each individual has one, or has many.

Individuals draw on knowledge of their surroundings to anticipate their partner’s response.
: in 'their surroundings', their would more likely be used as singular, since surrounding is often used in plural form. If their is assumed to be plural, then it would imply, by the usual construction of English, that there is a surrounding for each individual, but as mentioned, surrounding is often used in the plural. As a noun, I think "surroundings" is always plural.