So... I am the first author of this paper and I want to make 2 points...
1 - I just want to point out that while the shaving cream thing is maybe more flashy, phthalates are ubiquitous chemicals ALL around us. It's not just in shaving cream, it's in many many products. In fact, many of us breath in phthalate particles just from you know, existing and breathing.
2 - reducing men's chances of becoming fathers... is not technically something we did in this paper. The paper does not really suggest that higher exposure to this stuff reduces a man's fertility. What we did is look at sperm DNA methylation and in a small part relate that sperm DNA methylation to embryo quality in an IVF setting. If someone is really interested in male fertility, we'd have to look at male infertility diagnoses, IVF success, etc.
Here is a related paper directly looking at phthalates and embryo quality. https://academic.oup.com/humrep/article/32/1/65/2631391/Parental-contributions-to-early-embryo-development
Assuming this research is accurate the solution is fairly simple: Use a mechanical razor or remain traditional and try shaving oil or soap in place of chemical cream/foam-in-a-can. Another alternative is to use something like Shea Butter to shave with - you will probably never get a smoother shave...
Well the moral from this particular bent of science is pretty simple.
Get out of cities and away from man made products or you won't be making men much longer.