Edit: badly worded title. Please read "that's" as "that was", per the 20-Year Rule.
/u/sowser provided the magnificent answers in "How was the United Bermuda Party in control continuously from 1968 to 1998, and then start its slump?". I hadn't heard about white rule and oppression of black people other than in the big settler colonies (US, Australia, southern Africa). And I hadn't heard that one-party electoral rule was a field.
But along the way, they wrote
Apart from a single KFC and a McDonalds franchise at an American military base, fast food restaurants had been illegal in Bermuda for decades under the UBP. After leaving office, [former UBP premier] John Swan had applied to the government for permission to open a McDonalds franchise on the island - a decision Saul's [UBP] government signed off on in December 1995. This was a decision that scandalised the Bermudan public and the UBP's parliamentary party: it reeked of political favour-giving and was widely condemned as an illegal move, prompting a challenge in the country's highest courts. White voters in particular were outraged that the UBP appeared to be abandoning one of its most popular policies in favour of allowing one of its former leaders to make a profit.
Wait, fast-food restaurants were illegal and that was among the most popular of the policies around? Quick Googling suggests the Prohibited Restaurants Act of 1977, aimed at international fast-food chains specifically. (It also says "are" and "is", but 20-Year Rule, and I'm asking about the situation in 1995.)
How did that come in, and why, and why did people care so much? Especially when the McDonalds' at US Naval Air Station Bermuda was so very popular: "on one day in September 1991 more than 6,000 residents passed through its doors. That was more than 10 percent of the entire population at the time." source? And I've seen references to this act as "1977", yet some sort of bill was passed as a reaction in 1997 (source)? Interesting that the resulting law case went thru all the stages including the Privy Council in the UK.
Sorry - this is me being slightly unclear because I wrote the answer over several days!
It would have been more accurate of me to say that international fast food is illegal in Bermuda, yes; Bermuda itself does have a domestic street food industry, with an abundance of cafes and take-away venues across the island. The key thing is that these are all domestic enterprises (with the exception of the KFC on Queen Street in Hamilton), run primarily by people who live and work in Bermuda, using local branding that you won't find elsewhere in the world.
The KFC in Hamilton arrived in the 1970s and its presence was immediately controversial. It wasn't the food that KFC served that many Bermudans objected to per se - it was the presence of an international fast food chain that could undercut local businesses providing the same kind of street food, and what the success of KFC could mean for the future economic and social development of the island. My understanding is that there was no legislation passed in 1977, and that this 'factoid' on the internet circulates from a mistyping in one particular source where the author meant to type 1997 (you will find other books that say 1999, but the legislation was very much passed in 1997). What had happened is that under the UBP, the Bermuda Monetary Authority - the financial and corporate regulator for the country - had been consistently instructed to veto any application for the establishment of new fast food restaurants after the arrival of KFC. Without BMA approval, it was illegal for any new international franchise to open even if it had a local sponsor.
This was not a particular vendetta against international fast food. The decision to de facto outlaw these kind of companies from Bermuda was part of a wider policy adopted by the United Bermuda Party to keep Bermuda, for want of a better word, 'quaint'. The predominantly white middle class were strongly concerned with attracting the 'right' kind of tourists and residents to Bermuda, wanting to market the island to people who were looking for a quieter, dignified holiday or second home destination. There were serious concerns among this white elite that an explosion in international restaurant chains would attract the 'wrong kind' of tourist from the United States and undermine Bermuda's image as an idyllic destination with Old World charms. There were also serious worries about the potential harm done to Bermuda's own huge domestic leisure industry, with fast food outlets tempting people away from local casual food and hotel restaurants. Bermuda's UBP government had introduced similar measures against other international fads it considered 'gaudy', like outlawing neon signage for bars and restricting the use of cars (Bermuda's geography and roads are poorly suited to intense car traffic).
The policy was not popular in the sense that Bermuda voted for United Bermuda in election after election thinking consciously about it; it was popular in the sense that its attempted abandonment by the UBP in the mid-1990s alienated many voters, particularly in its traditional middle class base. Its popularity became apparent only when the policy was challenged and undermined - you don't know what you've got going for you until you've lost it, as the old adage goes. The outrage was compounded by the perception that the UBP was bending its long-term vision for Bermuda's prosperity to help its former leader make money at the expense of domestic Bermudan business (which tied into concerns among some voters that the UBP was increasingly worried about international investment and not enough about the local middle class it had been founded to protect the interests of). The 1997 legislation was the consequence of conservative elements in the UBP winning PLP support for a proposal to enshrine in primary legislation, not just in government policy, the illegality of opening a foreign restaurant on the island.
It's important to remember that Bermuda is a very small state. Even today there are only about 65,000 people living on the island. Electoral politics and government policy in such small states are a different beast to those of states with many millions of residents. In a country like Bermuda, political debate arises over both the kind of issues you would expect to hear in national debate in a country like the US and UK and also over bread-and-butter issues you might expect to be the purview of local politics in a bigger country. For example, in the most recent Bermudan election party manifestos - in addition to grand plans for economy and society - also contained promises like the development of a bus timetable app, changes to urban parks and construction projects in specific localities. In a country of 30million people the government allowing the construction of one McDonalds against its own guidance might not be too big of a deal; in Bermuda with its electorate of just a few tens of thousands, it could much more easily become a hot-button issue.
That isn't to say that many Bermudans didn't enjoy both KFC and the McDonalds that operated (illegally, technically) out of the US military base. There certainly were many residents of the island who were in favour of allowing international fast food onto the island, either for their own personal enjoyment or because they did not believe the scare mongering around the risks of letting such enterprises into the country. But the combination of McDonald's attempted arrival with the perceived corruption of the UBP playing favourites for former Premier John Swan helped created a storm around the issue and turned voters against the idea in the short-term even if they were not ideologically opposed to McDonalds arriving. Discontent was concentrated among the UBP's voter base, which made the scandal even worse for the government. KFC has been allowed to remain because the 1997 Act does not apply to any restaurant operating before 1996 (if KFC were to attempt to sell their premises to McDonalds or another transnational chain however, or dramatically rebrand, they would lose their license to trade).
It's also important to stress that just because 6,000 people passed through McDonalds at the US military base in 1991 doesn't mean that 6,000 Bermudan voters did; that number will have almost certainly included tourists, expats and non-voters (not to mention lifelong PLP voters) in significant numbers. And in a country like Bermuda where elections are decided by a few thousand swing voters in a two-party majoritarian system, it is possible for something to be unpopular on the whole with the electorate whilst still being very popular with certain sections of the population.
Hope this clarifies things for you!