There are many people in society which consider toy preference differences between the sexes as completely socialized. There is a very substantial amount of evidence which suggests that toy preference is, at least in part, due to biology, that evidence is summed up here:
Hormones have been shown to influence the behaviour in both girls and boys.
Girls with congenital adrenal hyperplasia who were exposed to high levels of androgen (male sex hormones) in the prenatal and early postnatal periods have been shown to prefer more male toys compared to their counterparts who were not exposed to these high levels of androgen.  There is also a correlation between fetal testosterone and the development of sex-typical play in children high levels of prenatal testosterone to increased male-typical play behaviour in boys and girls.  
Figure 1 shows the relationship between the testosterone levels and the Pre-School Activities Inventory score, the higher the scores represents more male-typical behaviour.
This evidence suggests that toy preference and gender-typical behaviour in general in, at least partly determined, by biological factors, more specifically the hormones the child is exposed to in utero.
Studies showing types of things infants look longer at (pre-socialisation) have found that male infants showed a stronger interest in the physical-mechanical mobile while the female infants showed a stronger interest in faces.  If these results are correct then they can explain differences in toy preference, as “male toys”, such as cars or balls fit the physical-mechanical category and “female toys”, such as dolls fit better with the face category. Table 0 Shows the results of this eye tracking experiment, showing preferences.
A widely cited study tracking the eye movements of neonates  compares what they consider a female toy and a male toy. I disagree that the toy they considered as female, they used a plush animal as a female toy, whereas I think it is a gender-neutral toy, I do agree, however, with them defining the truck as a male toy. Nether the less the results show that females were much less likely to look at the male toy than the doll, there the difference was insignificant for males, i.e. they look at the doll and the truck for similar amounts of time.
Figure 1 in the paper shows the results along with a small picture of the female and male toy so you can decide for yourself if the toys are correctly classified as male and female.
In order to see whether other animals had similar sex differences in toy preference, multiple studies have been done on primates. One of my favorite studies on toy preference  studied the amount of “contact time” male and female vervet monkeys had with neutral, masculine and feminine toys. The results showed that, consistent with human studies, males preferred male toys, females preferred female toys and there was not a significant difference between neutral toys. See figure 2 below.
A different study  studied on a different species of primate, they found that although males preferred masculine toys more, females showed no significant preference. Again they used a plush animal as a female toy, and I have to disagree with that classification, as did the authors of the other primate study I mentioned. 
Finally, the last evidence I will present is studies which indicate young children, pre-socialisation have a preference which is gender-specific.
These studies show that, even before socialization, there is a sex difference in toy preference, sometimes even as young as 9-months old.  
Table 1 shows the results from . Which compares a variety of different toys. As you would expect males played with the car, digger, and ball (physical and mechanical objects) more than girls, girls played with the doll more than boys (social object) and the plush toys were played with similar amounts. Notably, girls played with a cooking pot more than boys, however, I cannot think why that is the case.References:
 Berenbaum, Sheri A.; Hines, Melissa (1992). “Early Androgens Are Related to Childhood Sex-Typed Toy Preferences”. Psychological Science. 3 (3): 203–6.
 Auyeung, B.; Baron-Cohen, S.; Ashwin, E.; Knickmeyer, R.; Taylor, K.; Hackett, G.; Hines, M. (2009). “Fetal testosterone predicts sexually differentiated childhood behaviour in girls and in boys”. Psychol. Sci. 20 (2): 144–148
 Connellan, J., Baron-Cohen, S., Wheelwright, S., Batki, A. and Ahluwalia, J. (2000). Sex differences in human neonatal social perception. Infant Behaviour and Development, 23(1), pp.113-118.
 Alexander, G. M., Wilcox, T. & Woods, R. (2009). Sex differences in infants’ visual interest in toys. Archives of Sexual Behaviour, 38, 427–433
 Alexander GM, Hines M. Sex differences in response to children’s toys in nonhuman primates (cercopithecus aethiops sabaeus) Evolution and Human Behaviour. 2002;23:467–479.
 Hassett, J., Siebert, E. and Wallen, K. (2008). Sex differences in rhesus monkey toy preferences parallel those of children. Hormones and Behaviour, 54(3), pp.359-364.
 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2643016/#R1 (Accessed 19/05/2017)
 Todd, B., Barry, J. and Thommessen, S. (2016). Preferences for ‘Gender-typed’ Toys in Boys and Girls Aged 9 to 32 Months. Infant and Child Development.
 Servin, A., Bohlin, G. & Berlin, L. (1999). Sex differences in 1-, 3-, and 5-year-olds’ toy-choice in a structured play-session. Scandinavian Journal of Psychology, 40, 43–48
 Hönekopp, J. and Thierfelder, C. (2009). Relationships between digit ratio (2D:4D) and sex-typed play behavior in pre-school children. Personality and Individual Differences, 47(7), pp.706-710.