I'm looking for a fiction novel series about a submarine, being the USS Seawolf, finding the world in flames after a nuclear war.

This is likely to be On the Beach, sort of. Or an enormous rip-off thereof.

This was a 1957 novel by mainstream author Nevil Shute. It was made into a major film (Gregory Peck as the submarine captain) and remade in 2000 as a TV film.

What is similar is:

The submarine is running further and further south in the Pacific to find surviving people. A nuclear war in the northern hemisphere has produced a radioactive cloud which is remorselessly spreading south.

The submarine visits San Francisco (but everyone is dead there).

The submarine's name is USS Scorpion. In the novel there is one other surviving submarine, USS Swordfish in the Atlantic, which sends a couple of messages but is otherwise not involved in the plot.

Nothing else matches but there may be a reason for that:

Wikipedia says that it originally appeared as a 4-part series The Last Days on Earth in a British newspaper and was rewritten for the novel. This original series would be pretty inaccessible now but it would be my guess that you have read some reprinted form of this.

Try the Omega Sub series about the U.S.S Liberator by author J.D. Cameron. Book 5 called "Death Dive" deals with people in white shirts.

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Blurb

On the East Coast of a nuclear-decimated America, the Liberator sails into a savage zombie hell

U.S.S. Liberator—sailing the oceans of a nuclear-ravaged world on the most dangerous mission of all... survival!

A radio call for help has reached the U.S.S. Liberator from the shattered metropolis of New York. Two families have somehow managed to emerge unscathed from the fire and devastation of nuclear Armageddon. But rescuing them may prove an impossible task. For thousands of radiation-crazed "white shirts" have arisen from the ruins of the once-great city for one final, savage assault on the desperate survivors' stronghold—trapping Tom Donovan and his brave crew in the murderous center of an unrelenting reign of zombie terror.

Excerpt

Welcome to my nightmare

There were six corpses arranged bizarrely around the cabin. All had been stripped naked. All were rotted beyond recognition, their bones exposed in spots, ribbons of flesh hanging from their bodies. Two were seated on the settee, one was sprawled on the top of the dinette table, and two lay on the floor, their arms neatly aligned at their sides, their grisly, ragged lips pulled back to expose their yellowing teeth in ghastly grins of welcome.

"My God," Percy declared in horror.

The description is a mismatch as I am looking for the same series. The submarine was a Typhoon-class submarine that the US had purchased and turned into an underwater sea craft sub. The blue-green lasers were used as radar by the main ship as well as the mini-subs launched by it. There were underwater missiles. The story is not post-apocalyptic, but more a shift in global power where the US was fighting for its position. The ship was called the Sea-Wolf.

Update

I think you may have conflated two books; Stingray by Bill Keith and the Attack of the Seawolf series by Michael DiMercurio.

Stingray

Leviathan—the world's largest Typhoon-type vessel, a subcarrier equipped with the most advanced twenty-first-century laser technology and the ultimate weapon—a fast, agile fleet of SFV-4B Barracudas, the undersea version of the world's hottest new fighter plane.

The ultimate undersea challenge

Fresh from bloody battle off the coast of Cuba, Leviathan rides out to meet trouble at its source—Alexandria. There the formidable Islamic navy and its allies gather, sailing through the Strait of Gibraltar to block South American oil supplies and bring America to its knees.

Challenged by the Teigei, a Japanese supersub whose superior technology matches Leviathan's, Commander T. Morgan Gray, ace Navy pilot, must lead his intrepid men into a chilling undersea battle—one where only their daring, skill, and courage can snatch victory from the jaws of death and devastating final defeat.

Attack of the Seawolf

In the near future posited by this convincing techno-thriller, China has collapsed into civil war. The U.S. nuclear sub Tampa, sent into the Gulf of Chilhi to collect intelligence, is discovered and captured by the communists. The Navy's newest submarine, the Seawolf, embarks with a crack SEAL team for a rescue mission captained by Michael Pacino, who lost his last ship in last year's Voyage of the Devilfish. Now Pacino takes the Seawolf on a high-tech cutting-out expedition in the best tradition of 18th-century naval warfare

i think it might be the Seawolf by Cristobal--i'm looking for it, too. It was a fantasy, and part of a series, with strong female characters.