HSV1 doesn't protect against catching HSV2. If you have coldsores you are not protected from catching HSV2 genitally. Some unlucky people get both strains HSV1 and HSV2 in the same location (ex genitals).

But, If you have HSV1 orally (coldsores), you are more or less protected from catching HSV1 genitally. Same goes for the reverse, having HSV1 genitally protects you from catching it orally. Except almost everyone who has it HSV1 genitally also carries it orally asymptomatically because they caught it at the same time when they had no antibodies. About 80% of the population is hsv1 positive by 40.

Taking antivirals and wearing a condom cuts transmission of hsv2 significantly so if you're hsv2 positive, go on antivirals.