Can't save h5mu from Scirpy processed gex+bcr+tcr data if I copy airr into obs

Describe the bug

Can't save h5mu from Scirpy processed gex+bcr+tcr data if I copy airr into obs (i.e. tdata.obs = tdata.obs.join(ir.get.airr(tdata, tdata.obsm['airr'].fields))).
Unlike in #427 , I am on 0.13 and still suffer from the bug.

TypeError: Can't implicitly convert non-string objects to strings
Above error raised while writing key 'VJ_1_germline_alignment' of <class 'h5py._hl.group.Group'> to /

(it does this with many other columns, including all _call, _cigar columns)

To Reproduce

mdata = mu.MuData({'gex':adata.copy(),
       'tcr':tdata.copy(),
       'bcr':bdata.copy()})

ir.tl.chain_qc(mdata['tcr'])
ir.pp.ir_dist(mdata['tcr'], metric="hamming", sequence='nt', n_jobs=4, cutoff=20, key_added='ir_dist_nt_hamming_global')
ir.pp.ir_dist(mdata['tcr'], metric="identity", sequence='nt', n_jobs=4)

ir.tl.define_clonotypes(tdata, key_added='clone_id',
                        n_jobs=4, dual_ir='all', receptor_arms='all',
                        within_group=['receptor_type', 'donor_id_global'])

mdata['tcr'].obs = mdata['tcr'].obs.join(ir.get.airr(mdata['tcr'], mdata['tcr'].obsm['airr'].fields))

mdata.write(fname)

What else I've tried
Changing columns to categoricals

for mod in mdata.mod.keys():
    for col in mdata[mod].obs.columns:
        if re.findall(r'(V(?:D)?J_\d_\w_(?:call|cigar))', col):
            mdata[mod].obs[col] = mdata[mod].obs[col].astype('category')
            print(mod,':',col, sep='')
            
    mdata.update()

Expected behaviour
Save the file without problems

System

OS: Linux
Python version 3.9.16
Versions of libraries involved [Muon 0.1.5, Scirpy 0.13.0, Scanpy 1.9.3]

Additional context
Add any other context about the problem here.

Start with the mdata.write(fname) call after joining ir.get.airr(...) into mdata['tcr'].obs, and inspect how the VJ_1_germline_alignment and _call or _cigar columns are written. Reproduce with the supplied MuData and Scirpy workflow; done means the resulting h5mu file saves without the TypeError.