Short answer: no, you'll be fine.
There's this old adage that certain companies won't consider "contractors" for full time employment. That's only partially true at a very particular level.
I've had plenty of great candidates with traditional resumes with a heading statement of "seeking full time employment". Perhaps they have has a job listing from a well known consulting firm or as "Independent Consultant" with a few details. I don't dismiss these candidates. It's clear they are seeking full time employment. The consulting work is not a red flag. It's even a talking point in an interview to hear about their experiences in this area.
However, I have seen lots of resumes come in from recruiters where a candidate is marketing himself strictly as an independent contract professional. The header statement on their resume says "seeking contract employment" followed by multiple pages of short term gigs (3-12 months each).
In the rare times I've phone screened these professionals, they get really confused when I start talking about their career interests and our product strategy for the long term. They just want to come in, code, fix bugs, and get out. Then take a long vacation and move onto the next gig.
As such, they aren't the right fit to hire full time for my jobs. There's nothing wrong with these folks. It's just that I know from experience how to identify them from their resume structure and move on.
In other words, unless your resume becomes dominated by listings of gig work experiences instead of consolidating to a few brief lines (like you would any job experience), I doubt you'll get mistaken as a contractor.
When you originally spoke of gig work, I thought you meant "gig" in terms of software programming work. Now that I see your comment, I think you might have meant "gig" as in "Uber driver". That's perfectly fine too. Just leave this type of work off your resume. It's irrelevant for finding your next job and would only water down your resume. If it comes up in an interview, the answer is simple, "I was doing gig work to pay rent during my layoff caused by the pandemic." No one will question that.