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I was thinking about this the other day, what are the longest continuously played CFB rivalries interrupted by COVID-19?

According to this article from the NCAA, the 15 oldest rivalries in CFP are mostly Ivy League:

• Yale vs Princeton dates back to 1873, not played in 2020
• Yale vs Harvard dates back to 1875, not played in 2020
• Princeton vs Penn dates back to 1876, not played in 2020
• Princeton vs Harvard dates back to 1877, not played in 2020
• Yale vs Brown dates back to 1880, not played in 2020
• Harvard vs Dartmouth dates back to 1882, not played in 2020
• Lafayette vs Lehigh dates back to 1884, not played in 2020
• North Carolina vs Wake Forest dates back to 1888, UNC won 59-53 in 2020
• Miami, OH vs Cincy dates back to 1888, not played in 2020
• Cornell vs Columbia dates back to 1889, not played in 2020
• SDSU vs South Dakota dates back to 1889, not played in 2020 (I think, not sure)
• Army vs Navy dates back to 1890, Army won 15-0 in 2020
• Wisconsin vs Minnesota dates back to 1890, Wisconsin won 20-17 in 2020
• Minnesota vs Iowa dates back to 1891, Iowa won 35-7 in 2020
• Purdue vs Indiana dates back to 1891, not played in 2020

By my unofficial count it looks like 11 of the 15 oldest rivalries in CFB were not played in 2020. 

With the ending of the 102 year continuous rivalry with Michigan, here are Ohio State's longest continuously played rivalries:

• Penn State, 1993-present, 28 years
• Indiana, 2009-present, 12 years
• Michigan State, 2011-present, 10 years*
• Rutgers, 2014-present, 7 years
• Nebraska, 2016-present, 5 years
• Northwestern, 2018-present, 3 years**
• Clemson, 2019-present, 2 years***

*Michigan State:
This one is a little odd.  tOSU and MSU played regular season games in 2011 and 2012.  They were not scheduled to play in 2013 but they ended up meeting in the B1GCG.  From 2014-present they have played every year as members of the B1G-E.  

**Northwestern:
This one includes two B1GCG meetings (2018, 2020).  

***Clemson:
Both meetings were in bowls.  In fact this will be the fifth meeting of the Buckeyes and Tigers and all five have been in bowls:

• 1978 Gator Bowl:  Clemson won 17-15, Woody punched a kid and got fired.  
• 2014 Orange Bowl (2013 season):  Clemson won 40-35.  
• 2017 Fiesta Bowl/CFP semi-final (2016 season):  Clemson won 31-0.  
• 2020 Fiesta Bowl/CFP semi-final (2019 season):  Clemson won 29-23.  
• 2021 Sugar Bowl/CFP semi-final (2020 season):  TBD

How has this impacted your school's continuous rivalries?  

conference realignment has killed more of these than COVID

True.  

Ohio State's longest killed by that is Illinois.  The Bucks and Illini played a couple times before Ohio State was in what would become the B1G.  They had a 0-0 tie in Columbus in 1902 and a 46-0 Illini win in 1904 also in Columbus.  Then they missed each other in tOSU's first year in the conference (1913) but started playing every year in 1914.  That lasted 89 years (1914-2002) then ended.  Since then:

• 2003-2004:  missed
• 2005-2015:  played every year
• 2016:  missed
• 2017:  played
• 2018-2019:  missed
• 2020:  cancelled due to COVID-19

The Iowa v. Iowa State series restarted in 1977 after a 43-year hiatus, followed by 43-years straight playing this rivalry game. It was interrupted in 2020 by COVID-19. I am not an advocate for playing this game yearly. It would mean more if it were not played yearly.
Iowa State basically replaced Notre Dame as Iowa's nonconference rival. My feelings are that the Notre Dame series was more meaningful.