Subjectivity was very important to Romantics, as their literature is all about the subjective experience of nature, among other things. However, it is important to remember that this novel cannot be labelled so conveniently as merely a "Romantic" text. Frankenstein does not so easily slip into any one genre, and rather shares aspects of many. One of the crucial genres that it can be paired with is that of Gothic, and the first person perspective is particularly key in Gothic works of literature, as it allows the author to use the unreliable narrator as a key strategy in presenting a number of different conflicting views.
Narrative is a fascinating topic to consider in this novel as well, because like other Gothic classics such as Wuthering Heights, Shelley employs a framing narrative, in which different stories are nestled one inside the other like so many Russian dolls. Walton is in fact the overall narrator, but within his account, Frankenstein tells his story, then the creature tells his and the De Lacey narrative is also told through his account. There is a story-within-a-story-within-a-story-within-a-story. And if that is not complicated enough, the astute reader will have reason to believe that Frankenstein cannot be considered a reliable narrator in his section of the narrative. He presents himself as being completely prejudiced against his creature and his account distorts the creature. Note the following example from Chapter V, just after he has given life to the "wretch":
I beheld the wretch--the miserable monster whom I had created. He held up the curtain of the bed; and his eyes, if eyes they may be called, were fixed on me. His jaws opened, and he muttered some inarticulate sounds, while a grin wrinkled his cheeks. He might have spoken, but I did not hear; one hand was stretched out, seemingly to detain me, but I escaped, and rushed down stairs.
The key phrase to focus on in this quote is Frankenstein's interpretation of the monster's body language. He sees him with his hand stretched out and interprets this as the creature trying to physicaly stop him and assault him. Yet, given the fact that the monster has just been given life and Frankenstein is, to all intents and purposes, his father, is it not natural that he should stretch out his hand towards him through affection or love? Frankenstein constantly allows his own feelings of hatred and disgust to influence his account, making him an unreliable narrator, and this is something that is very important to realise when considering the first person narration of this novel.