The retired Grand Slam winning star and his wife Jenny became involved in an online petition after the death of Edinburgh investment manager Andrew McMenigall, 47, who was knocked off his bicycle by a lorry.
He died along with colleague Toby Wallace on the first day of a 960-mile fundraising cycle from Land's End to John O'Groats on July 1.
Then another friend, Douglas Brown, 79, of Leith, Edinburgh, suffered serious injuries and died three days later in hospital when he was hit by a truck while cycling on the B9080 Linlithgow to Kirkliston road, near Winchburgh Bing, West Lothian, on July 11.
Both men knew the couple through the Edinburgh Triathletes Club, where Mr McMenigall coached.
Mr Brown, a founding member of the club, had also trained Mrs Hastings for a number of years.
The experience has encouraged the Edinburgh couple, who are keen amateur riders, to lend their names to Cycle Law Scotland's (CLS) petition calling for a stricter liability law to protect Scotland's vulnerable road users by making motorists automatically at fault in collisions with cyclists.
The online campaign currently boasts almost 3500 signatures, with the group having set a target of gathering 5000.
The ex-rugby star said: "For Jenny and I, this is all about awareness. All road users need to be far more aware of cyclists who use the road. This can be as simple as giving more space to a cyclist when passing or overtaking but we also believe that cyclists also have a responsibility to be more visible to other road users.
"Cycle Law Scotland's (CLS) campaign will help to make our roads safer for all cyclists and we would urge as many people as possible to support this worthwhile cause."
CLS was set up by Brenda Mitchell, a keen cyclist and a personal injury lawyer.
The group is hoping to introduce a member's bill to the Scottish Parliament this autumn with the hope of changing the law.
Stricter liability laws would mean that in the event that a larger, faster moving vehicle is in collision with a cyclist or pedestrian, the driver should be presumed liable but if the injured party is under 14, over 70 or disabled, then the driver should be deemed fully liable.
The law is already widely enforced on continental Europe. Apart from the UK, only Cyprus, Malta, Romania and Ireland do not operate a system of strict liability for road users.
However, opponents of the proposals have argued that all road users should share an equal responsibility for safety.
Alan Douglas, a member of the Institute for Advanced Motoring, previously said: "This assumption that it is always the motorist at fault is absolutely breathtaking."
Ms Mitchell said: "I am delighted to welcome Scott and Jenny's support for the Road Share campaign. Road safety measures affect us all and I am pleased they are both able to recognise the benefits a strict liability regime could introduce.
"Our European neighbours are proving that the regime, which imposes responsibilities on those in control of dangerous objects to others, leads to increased awareness and greater consideration for vulnerable road users, therefore potentially reducing the number of tragic incidents.
"Losing someone you love in a road traffic collision is a tragedy I wouldn't wish upon anyone. With already nine cyclists killed in Scotland this year, now is the time for action, we must join our European counterparts."