OK, so have done a year-by-year check of the game scores from 1958 onward from the cfl.ca site (that’s as far back as they go) and if they are accurate, this is what I can tell you:
1958 - Ottawa was shut out against twice (and had a 3rd game where they only scored 1 point), BC came close (shut out once and scored 1 point in another game), and Toronto had two shutouts for, coming in consecutive games.
1959 - Weird year. Edmonton was shut out 12-0 by B.C. and then beat Saskatchewan 55-0 the next week. They also shut out Saskatchewan later that year, so if that is accurate then Farhan’s first tweet is incorrect (he himself has since acknowledged the error) and B.C. is not the first team to shut out the same opponent twice in a season (I cross referenced the league site with the Statscrew page that had the same info. Wikipedia did not have a team page for Edmonton or Saskatchewan for the 1959 season to verify it, and newspaper archives - the best resource, IMO - for that time are hard to find online without a lot of digging). Edmonton came close to getting a 3rd shutout, beating Winnipeg 16-1 (incidentally, the Bombers played again 2 days later and rebounded by putting up 61 points in a 61-8 thrashing of, you guessed it, Saskatchewan). Montreal was also shut out twice, once in the regular season and once in the playoffs. Like I said, weird year.
1960 - Edmonton had 1 shutout but were close 3 more times. They beat the lowly green Riders 19-1 and then blanked B.C. the following week 26-0, coming close to back-to-back clean sheets. Late in the year they gave up only 2 to Winnipeg and 2 more against Sask. again in consecutive games. The ‘Riders followed the first 19-1 loss mentioned above with a 27-0 loss to Winnipeg, so they almost had consecutive goose eggs.
1965 - Toronto is shut out twice, and the Bombers blank two opponents in the span of 3 games.
1966 - Ottawa, who had shut out Toronto earlier in the year, and Montreal, who had been shut out by Sask., play the lowest scoring game in CFL history, with the Alouettes winning 1-0.
1967 - Calgary blanks their opponents 3 times this year, Edmonton and Winnipeg each suffer a shut out loss twice.
1968 - Calgary earns 1 shut out in the regular season and another in the playoffs
1970 - Calgary becomes the last club before B.C. this season with multiple shut outs earned in a season, with 2.
1972 - For the first time since the CFL was established in 1958, there are no shut outs league-wide for the entire season. This will happen twice more this decade, in 1975 and 1978.
1980-81 - The CFL goes back-to-back seasons with no shutouts for any team for the first time. The non-shutout streak is broken the next year when Winnipeg wins in Montreal 36-0. That would be the only shutout in a 5 year span. In fact, there are only 5 shutouts league-wide in the whole decade, and the Bombers have 4 of them (‘82, ‘85, ‘86, and ‘88), with Edmonton dishing out the only other blank slate, also in 1988. The 1986 Bomber shutout is notable in that they beat Saskatchewan 56-0, the highest scoring shutout in league history.
1990-99 - Only 3 shutouts all decade, the most notable of which is Sacramento beating Baltimore 18-0 in the only game where a U.S. based team is involved in either end of a shutout.
Shutouts dried out even more in the 2000’s and beyond. Nothing too noteworthy before BC’s pair this season.