It is an issue that has come up before, notably after 20 children were killed at a Connecticut elementary school in late 2012. After the mass shooting at a concert in Las Vegas last year, California Treasurer John Chiang urged the state's teacher and public employee pensions to sell their holdings of companies that sell assault weapons, ammunition and gun accessories.
Those pensions are examining the issue.
Groups have pushed corporate America and the investment industry in the past to dump stocks to achieve other social goals, including campaigns to divest in fossil fuel companies, tobacco and apartheid-era South Africa.
Any association with the gun industry is becoming a heated topic again. First National Bank of Omaha said it won't renew a contract to issue a National Rifle Association-sponsored credit card after "customer feedback has caused us to review our relationship with the NRA."
Amy Domini, whose company developed the first index with standards that exclude gun makers, tobacco companies and others, said the issue may be seeing a turning point given the national outcry after the Florida shootings. "You get the sense that finally people are beginning to look at every tool in their toolbox."
A spokesman for the Florida state board told CNBC on Thursday that most of the pension's gun-maker stake is a result of its index investments. Out of $2.7 million in gun stocks it owns, $1.7 million is the result of investments in the Russell 3000 index, which holds stocks of gun makers.
Asset managers such as BlackRock have pinned the blame on the companies that develop the indexes fund companies track. "Index providers are responsible for the construction of their indices. As a fiduciary, we have a responsibility to replicate the indices our clients choose to invest in. As a result, we invest in a company as long as that company is in the relevant index," the company said Thursday.
Often big pensions ask a fund manager to block certain investments if they want to avoid them. BlackRock said it has $200 billion of assets in portfolios customized to exclude weapons makers.
John Kuczwanski, the Florida state board's spokesman, said while the pension blocks investments in federally sanctioned countries such as Libya it doesn't have any restrictions on investing in gun makers. And while divesting gun stocks from the pension has been brought up in the debate about guns over the last week, it's not in the works.
"As fiduciaries our sole responsibility is to the plan beneficiaries," he said.
In New Jersey, state Sen. Vin Gopal introduced a bill modeled after a recent law barring the state's pension from investing in businesses that boycott or otherwise harm Israel.
Gopal told CNBC gun makers shouldn't benefit from state investment in them if they aren't part of the solution to responsible gun ownership. "We want to send a message."
The bill would bar the state from investing assets of any pension or annuity fund in companies that make firearms or ammunition. New Jersey's pension isn't listed as an owner of Sturm Ruger or American Outdoor Brands, according to data by FactSet. But the New Jersey Division of Investment is listed having a 0.08 percent stake in Vista Outdoor.
In New York, there have been efforts to divest from gun makers with mixed results. In New York City three of five public pensions sold their gun-maker stocks, while New York State Teachers Retirement System continues to hold shares of gun makers because its investments track indexes.
"No decision has been made on divestment of gun stocks from our portfolios," John Cardillo, the pension's spokesman, told CNBC.