IMO it's nothing like that. There's no significant difference in availability of birth control in red vs blue states.
It's that in red states the pandemic was an extended party and vacation with everyone having extra money.
No entertainment places closed. There was no overall feeling of anxiety. Bars, Restaurants, vacation spots were more packed than ever.
Young people partied, worked from home and got thousands and thousands of dollars in free money. Pretty much everyone I know that was in the category of "probably going to have kids at some point" went ahead and had kids. My close friends from high school to college in red states span a range of about 8 years and almost all had kids. All planned and on purpose because it really just felt like an ideal time.
It was also a great hospital experience! No guests, labor and delivery was over staffed. Hospital, other than the barrier separated COVID area was completely empty.
On the other hand I have friends in blue states and areas that literally stayed home for months. Some people didn't even go out to eat for a year.
Schools were also closed for over a year in some blue states. Red States just had some schools close for like 2 months.