Can a person be persuaded to become gay?

The article you linked (Hamer, et al. 1993 [Open Access PDF]) was cited in Mills (2019) [Open Access PDF] which states,

Work in the 1990s isolated a relationship with the Xq28 region on the X chromosome (5 [Hu, et al. (1995)], 6 [Hamer, et al. 1993]). Subsequent studies found similarity in the sexual orientation of identical twins, with genetics explaining 18% (for women) and 37% (for men), with the remainder accounted for by directly shared environments (such as family or school) and nonshared environments (such as legalization or norms regarding same-sex behavior) (7 [Långström, et al. (2010) Open Access PDF]). Many of these studies could not be replicated, and although twin and family studies found a genetic basis, they could not isolate variants associated with same-sex orientation at specific genetic loci.

Mills (2019) also reports that,

On page 882 of this issue, Ganna et al. (3 [Ganna, et al. (2019) Open Access PDF]) report the largest study to date, comprising almost half a million individuals in the United Kingdom and United States, identifying genetic variants associated with same-sex sexual behavior. They provide evidence that genetic variation accounts for a small fraction of same-sex sexual behavior and uncover a relationship to the regulation of the sex hormones testosterone and estrogen as well as sex-specific differences. They also reveal complexity of human sexuality.

There is also a comment on this study (Hamer, et al. 2021 Open Access PDF) and response (Ganna, et al. 2021 Open Access) is also available for your review.

With all this in mind, in review of Hamer et al. (1993) you linked to, the answer to the question Can hocd change sexual orientation? still stands that,

[N]othing and nobody can make you homosexual, bisexual or heterosexual

The thing is, genetics has nothing to do with persuading someone to be gay other than the fact that if genetics were involved, persuasion cannot be effective.

So with that in mind, reviewing the rest of the answer to the question Can hocd change sexual orientation?, it still stands that,

[N]othing and nobody can make you homosexual, bisexual or heterosexual

References

Ganna, A., Verweij, K. J., Nivard, M. G., Maier, R., Wedow, R., Busch, A. S., ... & Zietsch, B. P. (2019). Large-scale GWAS reveals insights into the genetic architecture of same-sex sexual behavior. Science, 365(6456). https://doi.org/10.1126/science.aat7693

Ganna, A., Verweij, K. J., Nivard, M. G., Maier, R., Wedow, R., Busch, A. S., ... & Zietsch, B. P. (2021). Response to Comment on “Large-scale GWAS reveals insights into the genetic architecture of same-sex sexual behavior”. Science, 371(6536). https://doi.org/10.1126/science.aba5693

Hamer, D. H., Hu, S., Magnuson, V. L., Hu, N., & Pattatucci, A. M. (1993). A linkage between DNA markers on the X chromosome and male sexual orientation. Science, 261(5119), 321-327. https://doi.org/10.1126/science.8332896

Hamer, D., Mustanski, B., Sell, R., Sanders, S. A., & Garcia, J. R. (2021). Comment on “Large-scale GWAS reveals insights into the genetic architecture of same-sex sexual behavior”. Science, 371(6536). https://doi.org/10.1126/science.aba2941

Hu, S., Pattatucci, A. M., Patterson, C., Li, L., Fulker, D. W., Cherny, S. S., ... & Hamer, D. H. (1995). Linkage between sexual orientation and chromosome Xq28 in males but not in females. Nature genetics, 11(3), 248-256. https://doi.org/10.1038/ng1195-248

Långström, N., Rahman, Q., Carlström, E., & Lichtenstein, P. (2010). Genetic and environmental effects on same-sex sexual behavior: A population study of twins in Sweden. Archives of sexual behavior, 39(1), 75-80 https://doi.org/10.1007/s10508-008-9386-1

Mills, M. C. (2019). How do genes affect same-sex behavior?. Science, 365(6456), 869-870. http://doi.org/10.1126/science.aay2726