A specific method for exclusion of strength and body size from traits important for reproductive success will depend on your species physiology, habitat, and social structure. For example, hidden ovulation (like humans have) increases the necessity for the monopolisation of females by males. A habitat full of dangerous predators and sex roles where males are the main protectors will favour strength (for fight) or agility and stamina (for flight). Social structures with polygamous mating will most likely favour strength if violence is the main method of harem protection.

Another important aspect is male-male interactions. Species where male combat is common tend to have males stronger and bigger than females. If your male hominids do not use violence to win against other males differences in strength and body size will be less pronounced.

A specific method for exclusion of strength and body size from traits important for reproductive success will depend on your species physiology, habitat, and social structure. Some examples of things that can affect reproductive success:

• hidden ovulation (like humans have) increases the necessity for the monopolisation (not sharing one's mate with others) of females by males. As seen in the comments this point is a bit tricky, so I will list some additional relevant points to consider:

  1. If males do not know when females are in heat, they need to avoid sharing female with other males if they want to make sure that the offsprings are theirs. Therefore, the necessity for monopolisation in terms of reproductive success. This does not mean, however, that hidden ovulation on its own will inevitably lead to sexual dimorphism.
  2. Monopolisation can be achieved through various means, including non-violent ones such as marriage. Violent means are most likely to lead to sexual dimorphism related to strength and size, while non-violent means may promote other traits (for example, intelligence).
  3. Hidden ovulation strengthens the position of females as choosers because it helps to conceal the fact that the regular mating partner is not the real father of offsprings. This may affect sexual dimorphism depending on the preferences of females.
  4. Hidden ovulation in isolation from other factors does not necessarily lead to sexual dimorphism. Its role should be examined in the context of all other factors.
  5. Hidden ovulation does not lead to monogamy or even stable mating partners. The majority of mammals that have concealed ovulation are promiscuous. One of the theories suggests that hidden ovulation evolved in order to increase paternal investment and decrease infanticide. This may contribute to greater sexual dimorphism if biological fathers and de facto caretakers are different males (for example, females may choose more aggressive males as fathers and less aggressive males as caretakers).

• a habitat full of dangerous predators and sex roles where males are the main protectors will favour strength (for fight) or agility and stamina (for flight).

• social structures with polygamous mating will most likely favour strength if violence is the main method of harem protection.

Another important aspect is male-male interactions. Species where male combat is common tend to have males stronger and bigger than females. If your male hominids do not use violence to win against other males differences in strength and body size will be less pronounced.

Please do not see this answer as a blueprint for the evolution of your species. I just listed some examples of factors that can influence sexual dimorphism. Please also note that there is no one simple solution. There are always numerous factors affecting evolution. You should look at as many of them as possible and try to see how they interact. It is absolutely normal to have several contradicting forces shaping the evolution of a species. The outcome always depends on a combination of various factors and their interactions.

The two main factors would be:

• sexual selection;
• reproductive success non-dependent on physical strength and body size.

Sexual selection is natural selection based on preferences for sexual partners. It is speculated that sexual selection is the main reason for higher-pitched voice and sub-optimal fat distribution in human females.

Your hypothetical hominids need to favour traits that you listed as desirable and select for them. As time goes by those traits will become dominant in the general population.

Reproductive success refers to an individual's ability to produce offsprings that become part of the breeding population once they mature. If greater strength and/or bigger body size result in reproductive success your species will eventually evolve to be bigger and stronger. Sexual dimorphism will occur if requirements for reproductive success differ between sexes.

A specific method for exclusion of strength and body size from traits important for reproductive success will depend on your species physiology, habitat, and social structure. For example, hidden ovulation (like humans have) increases the necessity for the monopolisation of females by males. A habitat full of dangerous predators and sex roles where males are the main protectors will favour strength (for fight) or agility and stamina (for flight). Social structures with polygamous mating will most likely favour strength if violence is the main method of harem protection.

Another important aspect is male-male interactions. Species where male combat is common tend to have males stronger and bigger than females. If your male hominids do not use violence to win against other males differences in strength and body size will be less pronounced.

The two main factors would be:

• sexual selection;
• reproductive success non-dependent on physical strength and body size.

Sexual selection is natural selection based on preferences for sexual partners. It is speculated that sexual selection is the main reason for higher-pitched voice and sub-optimal fat distribution in human females.

Your hypothetical hominids need to favour traits that you listed as desirable and select for them. As time goes by those traits will become dominant in the general population.

Reproductive success refers to an individual's ability to produce offsprings that become part of the breeding population once they mature. If greater strength and/or bigger body size result in reproductive success your species will eventually evolve to be bigger and stronger. Sexual dimorphism will occur if requirements for reproductive success differ between sexes.

A specific method for exclusion of strength and body size from traits important for reproductive success will depend on your species physiology, habitat, and social structure. For example, hidden ovulation (like humans have) increases the necessity for the monopolisation of females by males. A habitat full of dangerous predators and sex roles where males are the main protectors will favour strength (for fight) or agility and stamina (for flight). Social structures with polygamous mating will most likely favour strength if violence is the main method of harem protection.

Another important aspect is male-male interactions. Species where male combat is common tend to have males stronger and bigger than females. If your male hominids do not use violence to win against other males differences in strength and body size will be less pronounced.

I thought about it a little bit more and it seems that it might be hard to keep the same aesthetics as modern humans if you want to equalise strength.

One of the main reasons for the greater physical strength of males compared to females is body composition: Males have higher muscle-mass to body-mass ratio (men have more muscles than women when adjusted for body size and weight). If you want women to have body curves and attractive big breasts you will have to sacrifice muscles and exchange them for body fat.

Androgynous appearance might be more conducive to your ideal of equal physical strength and performance.