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What is it to eschew nominalism for realism?

It is to allow that "distinctions of logical type have counterparts in extra-linguistic reality" ("Some Reflections on Metaphysics and Reality": 26).

What the realist thus allows is not simply the objective reality of the universal, but "the objective reality of the distinction between universal and particular. . . The basic issue is the ontological status of logical polarities, e.g., universal-particular. But then the related contrasts actual-possible, or possible-necessary, or contingent-necessary must be similarly treated. The 'nitty-gritty' of the issue concerns the status of modality. Tho~ho Those who say that only propositions are necessary or contingent are the hard-core (or hopeless) nominalists....
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"One more steF}tstep: modal distinctions are ultimately coincident with
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temporal ones. The actual is the past, the possible is the future" (CSPM: 61).