Will increased level of ocean acidity lead to more frequent acid rain?

Essentially no. Acid rain was especially a problem when coal and other industries let up vast amout of sulphur which made strong sulphuric acid rain which could kill trees. Volcanos can also have similar effects, and some industrial regions still create acid rain. There are maps available.

So, as the energy industry becomes solar/wind based, there will be less acid rain.

There is another source of acid in the rain, which is not due to the oceans: CO2... it causes the rain to wear down the mountains and it causes erosion. The rocks and alkaline minerals are one of the carbon sinks that bind to atmospheric CO2.

Current CO2 emissions are around 40 billion tons a year; natural weathering absorbs roughly 1.1 billion tons.

Higher CO2 in the air does make the rain more acid, it just dissolves alkaline rocks i.e. limestone a lot more efficiently.

More likely, it works the other way: increased acid-forming compounds in the atmosphere are the cause of more ocean acidification.

Pio et al. [1] report measurements of sulfur and nitrogen compounds in air masses that they traced to either continental or oceanic origins. They report that the lowest levels of these compounds were from ocean-origin air masses, indicating that the ocean is absorbing acid-rain causing pollutants such as sulfur dioxide. Even so, levels of these compounds over the oceans has increased in recent years, likely from increased pollution on land.

In this answer it is noted that increasing acidity can alter the salt composition of the ocean, producing more acidic species (such as $text{H}_2text{PO}_4^-$ ions). However, these tend to remain dissolved in the water rather than evaporate into the atmosphere.

Reference

1. Casimiro A. Pio, Mário A.Cerqueira, Luis M.Castro, Maria L.Salgueiro, "Sulphur and nitrogen compounds in variable marine/continental air masses at the southwest European coast", Atmospheric Environment Volume 30, Issue 18, September 1996, Pages 3115-3127.